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# MCQ in Analytic Geometry: Parabola, Ellipse and Hyperbola Part 1 | Math Board Exam

This is the Multiple Choice Questions Part 1 of the Series in Analytic Geometry: Parabola, Ellipse and Hyperbola topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

• MCQ in Rectangular coordinates system | MCQ in Distance Formula | MCQ in Distance between two points in space | MCQ in Slope of a Line | MCQ in Angle between two lines | MCQ in Distance between a point and a line | MCQ in Distance between two lines | MCQ in Division of line segment | MCQ in Area by coordinates | MCQ in Lines | MCQ in Conic sections | MCQ in Circles

#### Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

Problem 1: CE Board May 1995

What is the radius of the circle x2 + y2 โ 6y = 0?

A. 2

B. 3

C. 4

D.5

Solution: Review: Solution for Number 1

Problem 2: CE Board November 1995

What are the coordinates of the center of the curve x2 + y2 โ 2x โ 4y โ 31 = 0?

A. (-1, -1)

B. (-2, -2)

C. (1, 2)

D. (2, 1)

Solution: Review: Solution for Number 2

Problem 3:

A circle whose equation is x2 + y2 + 4x +6y โ 23 = 0 has its center at

A. (2, 3)

B. (3, 2)

C. (-3, 2)

D. (-2, -3)

Solution: Review: Solution for Number 3

Problem 4: ME Board April 1998

What is the radius of a circle with the ff. equation: x2 โ 6x + y2 โ 4y โ 12 = 0

A. 3.46

B. 7

C. 5

D.6

Solution: Review: Solution for Number 4

Problem 5: ECE Board April 1998

The diameter of a circle described by 9x2 + 9y2 = 16 is?

A. 4/3

B. 16/9

C. 8/3

D. 4

Solution: Review: Solution for Number 5

Problem 6: CE Board May 1996

How far from the y-axis is the center of the curve 2x2 + 2y2 +10x โ 6y โ 55 = 0

A. -2.5

B. -3.0

C. -2.75

D. -3.25

Solution: Review: Solution for Number 6

Problem 7:

What is the distance between the centers of the circles x2 + y2 + 2x + 4y โ 3 = 0 and x2 + y2 โ 8x โ 6y + 7 = 0?

A. 7.07

B. 7.77

C. 8.07

D. 7.87

Solution: Review: Solution for Number 7

Problem 8: CE Board November 1993

The shortest distance from A (3, 8) to the circle x2 + y2 + 4x โ 6y = 12 is equal to?

A. 2.1

B. 2.3

C. 2.5

D. 2.7

Solution: Review: Solution for Number 8

Problem 9: ME Board October 1996

The equation circle x2 + y2 โ 4x + 2y โ 20 = 0 describes:

A. A circle of radius 5 centered at the origin.

B. An eclipse centered at (2, -1).

C. A sphere centered at the origin.

D. A circle of radius 5 centered at (2, -1).

Solution: Review: Solution for Number 9

Problem 10: EE Board April 1997

The center of a circle is at (1, 1) and one point on its circumference is (-1, -3). Find the other end of the diameter through (-1, -3).

A. (2, 4)

B. (3, 5)

C. (3, 6)

D. (1, 3)

Solution: Review: Solution for Number 10

Problem 11:

Find the area (in square units) of the circle whose equation is x2 + y2 = 6x โ 8y.

A. 20 ฯ

B. 22 ฯ

C. 25 ฯ

D. 27 ฯ

Solution: Review: Solution for Number 11

Problem 12:

Determine the equation of the circle whose radius is 5, center on the line x = 2 and tangent to the line 3x โ 4y + 11 = 0.

A. (x โ 2)2 + (y โ 2)2 = 5

B. (x โ 2)2 + (y + 2)2 = 25

C. (x โ 2)2 + (y + 2)2 = 5

D. (x โ 2)2 + (y โ 2)2 = 25

Solution: Review: Solution for Number 12

Problem 13:

Find the equation of the circle with the center at (-4, -5) and tangent to the line 2x + 7y โ 10 = 0.

A. x2 + y2 + 8x โ 10y โ 12 = 0

B. x2 + y2 + 8x โ 10y + 12 = 0

C. x2 + y2 + 8x + 10y โ 12 = 0

D. x2 + y2 โ 8x + 10y + 12 = 0

Solution: Review: Solution for Number 13

Problem 14: ECE Board April 1998

Find the value of k for which the equation x2 + y2 + 4x โ 2y โ k = 0 represents a point circle.

A. 5

B. 6

C. -6

D. -5

Solution: Review: Solution for Number 14

Problem 15: ECE Board April 1999

3x2 + 2x โ 5y + 7 = 0. Determine the curve.

A. Parabola

B. Ellipse

C. Circle

D. Hyperbola

Solution: Review: Solution for Number 15

Problem 16: CE Board May 1993, CE Board November 1993, ECE Board April 1994

The focus of the parabola y2 = 16x is at

A. (4, 0)

B. (0, 4)

C. (3, 0)

D. (0, 3)

Solution: Review: Solution for Number 16

Problem 17: CE Board November 1994

Where is the vertex of the parabola x2 = 4(y โ 2)?

A. (2, 0)

B. (0, 2)

C. (3, 0)

D. (0, 3)

Solution: Review: Solution for Number 17

Problem 18: ECE Board April 1994, ECE Board April 1999

Find the equation of the directrix of the parabola y2 = 16x.

A. x = 2

B. x = -2

C. x = 4

D. x = -4

Solution: Review: Solution for Number 18

Problem 19:

Given the equation of a parabola 3x + 2y2 โ 4y + 7 = 0. Locate its vertex.

A. (5/3, 1)

B. (5/3, -1)

C. -(5/3, -1)

D. (-5/3, 1)

Solution: Review: Solution for Number 19

Problem 20: ME Board April 1997

In the equation y = – x2 + x + 1, where is the curve facing?

A. Upward

B. Facing left

C. Facing right

D. Downward

Solution: Review: Solution for Number 20

Problem 21: CE Board May 1995

What is the length of the length of the latus rectum of the curve x2 = 20y?

Solution: Review: Solution for Number 21

Problem 22: EE Board October 1997

Find the location of the focus of the parabola y2 + 4x โ 4y โ 8 = 0.

A. (2.5, -2)

B. (3, 1)

C. (2, 2)

D. (-2.5, -2)

Solution: Review: Solution for Number 22

Problem 23: ECE Board April 1998

Find the equation of the axis of symmetry of the function y = 2x2 โ 7x + 5.

A. 7x + 4 = 0

B. 4x + 7 = 0

C. 4x โ 7 = 0

D. x โ 2 = 0

Solution: Review: Solution for Number 23

Problem 24:

A parabola has its focus at (7, -4) and directrix y = 2. Find its equation.

A. x2 + 12y โ 14x + 61 = 0

B. x2 โ 14y + 12x + 61 = 0

C. x2 โ 12x + 14y + 61 = 0

D. none of these

Solution: Review: Solution for Number 24

Problem 25:

A parabola has its axis parallel to the x-axis, vertex at (-1, 7) and one end of the latus rectum at (-15/4, 3/2). Find its equation.

A. y2 โ 11y + 11x โ 60 = 0

B. y2 โ 11y + 14x โ 60 = 0

C. y2 โ 14y + 11x + 60 = 0

D. none of these

Solution: Review: Solution for Number 25

Problem 26: ECE Board November 1997

Compute the focal length and the length of the latus rectum of the parabola y2 + 8x โ 6y + 25 = 0.

A. 2, 8

B. 4, 16

C. 16, 64

D. 1, 4

Solution: Review: Solution for Number 26

Problem 27:

Given a parabola (y โ 2)2 = 8(x โ 1). What is the equation of its directrix?

A. x = -3

B. x = 3

C. y = -3

D. y = 3

Solution: Review: Solution for Number 27

Problem 28: ME Board October 1997

The general equation of a conic section is given by the following equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. A curve maybe identified as an ellipse by which of the following conditions?

A. B2 โ 4AC < 0

B. B2 โ 4AC = 0

C. B2 โ 4AC > 0

D. B2 โ 4AC = 1

Solution: Review: Solution for Number 28

Problem 29: CE Board November 1994

What is the area enclosed by the curve 9x2 + 25y2 โ 225 = 0?

A. 47.1

B. 50.2

C. 63.8

D. 72.3

Solution: Review: Solution for Number 29

Problem 30: ECE Board April 1998

Point P (x, y) moves with a distance from point (0, 1) one-half of its distance from line y = 4. The equation of its locus is?

A. 2x2 โ 4y2 = 5

B. 4x2 + 3y2 = 12

C. 2x2 + 5y3 = 3

D. x2 + 2y2 = 4

Solution: Review: Solution for Number 30

Problem 31:

The lengths of the major and minor axes of an ellipse are 10 m and 8 m, respectively. Find the distance between the foci.

A. 3

B. 4

C. 5

D. 6

Solution: Review: Solution for Number 31

Problem 32:

The equation 25x2 + 16y2 โ 150x + 128y + 81 = 0 has its center at?

A. (3, -4)

B. (3, 4)

C. (4, -3)

D. (3, 5)

Solution: Review: Solution for Number 32

Problem 33: EE Board October 1997

Find the major axis of the ellipse x2 + 4y2 โ 2x โ 8y + 1 = 0.

A. 2

B. 10

C. 4

D. 6

Solution: Review: Solution for Number 33

Problem 34: CE Board May 1993

The length of the latus rectum for the ellipse is equal to?

A. 2

B. 3

C. 4

D. 5

Solution: Review: Solution for Number 34

Problem 35:

An ellipse with an eccentricity of 0.65 and has one of its foci 2 units from the center. The length of the latus rectum is nearest to?

A. 3.5 units

B. 3.8 units

C. 4.2 units

D. 3.2 units

Solution: Review: Solution for Number 35

Problem 36:

An earth satellite has an apogee of 40,000 km and a perigee of 6,600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci?

A. 0.46

B. 0.49

C. 0.52

D. 0.56

Solution: Review: Solution for Number 36

Problem 37: ECE Board April 1998

The major axis of the elliptical path in which the earth moves around the sun is approximately 168,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

A. 93,000,000 miles

B. 91,450,000 miles

C. 94,335,100 miles

D. 94,550,000 miles

Solution: Review: Solution for Number 37

Problem 38: CE Board November 1992

The earthโs orbit is an ellipse with the sun at one of the foci. If the farthest distance of the sun from the earth is 105.5 million km and the nearest distance of the sun from the earth is 78.25 million km, find the eccentricity of the ellipse.

A. 0.15

B. 0.25

C. 0.35

D. 0.45

Solution: Review: Solution for Number 38

Problem 39:

An ellipse with center at the origin has a length of major axis 20 units. If the distance from center of ellipse to its focus is 5, what is the equation of its directrix?

A. x = 18

B. x = 20

C. x = 15

D. x = 16

Solution: Review: Solution for Number 39

Problem 40:

What is the length of the latus rectum of 4x2 + 9y2 + 8x โ 32 = 0?

A. 2.5

B. 2.7

C. 2.3

D. 2.9

Solution: Review: Solution for Number 40

Problem 41: EE Board October 1993

4x2 โ y2 = 16 is the equation of a/an?

A. parabola

B. hyperbola

C. circle

D. ellipse

Solution: Review: Solution for Number 41

Problem 42: EE Board October 1993

Find the eccentricity of the curve 9x2 โ 4y2 โ 36x + 8y = 4.

A. 1.80

B. 1.92

C. 1.86

D. 1.76

Solution: Review: Solution for Number 42

Problem 43: CE Board November 1995

How far from the x-axis is the focus F of the hyperbola x2 โ 2y2 + 4x + 4y + 4 = 0?

A. 4.5

B. 3.4

C. 2.7

D. 2.1

Solution: Review: Solution for Number 43

Problem 44: EE Board October 1994

The semi-transverse axis of the hyperbola is?

A. 2

B. 3

C. 4

D. 5

Solution: Review: Solution for Number 44

Problem 45: CE Board May 1996

What is the equation of the asymptote of the hyperbola?

A. 2x โ 3y = 0

B. 3x โ 2y = 0

C. 2x โ y = 0

D. 2x + y = 0

Solution: Review: Solution for Number 45

Problem 46: EE Board April 1994

Find the equation of the hyperbola whose asymptotes are y = ยฑ 2x and which passes through (5/2, 3).

A. 4x2 + y2 + 16 = 0

B. 4x2 + y2 โ 16 = 0

C. x2 โ 4y2 โ 16 = 0

D. 4x2 โ y2 = 16

Solution: Review: Solution for Number 46

Problem 47:

Find the equation of the hyperbola with vertices (-4, 2) and (0, 2) and foci (-5, 2) and (1, 2).

A. 5x2 โ 4y2 + 20x +16y โ 16 = 0

B. 5x2 โ 4y2 + 20x โ 16y โ 16 = 0

C. 5x2 โ 4y2 โ 20x +16y + 16 = 0

D. 5x2 + 4y2 โ 20x +16y โ 16 = 0

Solution: Review: Solution for Number 47

Problem 48:

Find the distance between P1 (6, -2, -3) and P2 (5, 1, -4).

A. 11

B. โ11

C. 12

D. โ12

Solution: Review: Solution for Number 48

Problem 49:

The point of intersection of the planes x + 5y โ 2z = 9; 3x โ 2y + z = 3 and x + y + z = 2 is at?

A. (2, 1, -1)

B. (2, 0, -1)

C. (-1, 1, -1)

D. (-1, 2, -1)

Solution: Review: Solution for Number 49

Problem 50: ME Board April 1997

What is the radius of the sphere center at the origin that passes the point 8, 1, 6?

A. 10

B. 9

C. โ101

D. 10.5

Solution: Review: Solution for Number 50

Problem 51:

The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is?

A. x2 + y2 + z2 +6x โ 4y โ 8z = 36

B. x2 + y2 + z2 +6x โ 4y โ 8z = 7

C. x2 + y2 + z2 +6x โ 4y + 8z = 6

D. x2 + y2 + z2 +6x โ 4y + 8z = 36

Solution: Review: Solution for Number 51

Problem 52: EE Board April 1997

Find the polar question of the circle, if its center is at (4, 0) and the radius 4.

A. r โ 8 cos ฮธ = 0

B. r โ 6 cos ฮธ = 0

C. r โ 12 cos ฮธ = 0

D. r โ 4 cos ฮธ = 0

Solution: Review: Solution for Number 52

Problem 53: ME Board October 1996

What are the x and y coordinates of the focus of the iconic section described by the following equation? (Angle ฮธ corresponds to a right triangle with adjacent side x, opposite side y and the hypotenuse r.)ย  r sin2 ฮธ = cos ฮธ

A. (1/4, 0)

B. (0, ฯ/2)

C. (0, 0)

D. (-1/2, 0)

Solution: Review: Solution for Number 53

Problem 54:

Find the polar equation of the circle of radius 3 units and center at (3, 0).

A. r = 3 cos ฮธ

B. r = 3 sin ฮธ

C. r = 6 cos ฮธ

D. r = 9 sin ฮธ

Solution: Review: Solution for Number 54

Problem 55: EE Board October 1997

Given the polar equation r = 5 sin ฮธ. Determine the rectangular coordinate (x, y) of a point in the curve when ฮธ is 30ยบ.

A. (2.17, 1.25)

B. (3.08, 1.5)

C. (2.51, 4.12)

D. (6, 3)

Solution: Review: Solution for Number 55

### Online Questions and Answers in Analytic Geometry: Parabola, Ellipse and Hyperbola Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Analytic Geometry: Parabola, Ellipse and Hyperbola
PART 1: MCQ from Number 1 โ 50                                Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                           Answer key: PART 2

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