﻿ Engineering Entrance Exam Question and Answers | Conic Section - Zigya

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# Conic Section

#### Multiple Choice Questions

21.

For the Hyperbola  which of the following remains constant when α varies?

• Eccentricity

• Directrix

• Abscissae of vertices

• Abscissae of vertices

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22.

The equation of a tangent to the parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

• (−1, 1)

• (0, 2)

• (2, 4)

• (2, 4)

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23.

The locus of the vertices of the family of parabolas

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24.

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

• 3/5

• 1/5

• 2/5

• 2/5

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25.

If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is

• x2 + y2 + 2x − 2y − 47 = 0

• x2 + y2 + 2x − 2y − 62 = 0

• x2 + y2 − 2x + 2y − 62 = 0

• x2 + y2 − 2x + 2y − 62 = 0

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26.

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π/3  at its centre is

• x2+y2 = 3/2

• x2 + y2 = 1

• x2+y2 = 27/4

• x2+y2 = 27/4

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27.

Area of the greatest rectangle that can be inscribed in the ellipse

• 2ab

• ab

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28.

Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is

• y2 – 4x + 2 = 0

• y2 + 4x + 2 = 0

• x2 + 4y + 2 =

• x2 + 4y + 2 =

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29.
• an ellipse

• a circle

• a straight line

• a straight line

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30.

The locus of a point P (α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola

• an ellipse

• a circle

• a parabola

• a parabola

219 Views