﻿ Engineering Entrance Exam Question and Answers | Conic Section - Zigya

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# Conic Section

#### Multiple Choice Questions

361.

A circle having centre at the origin passes through the three vertices of an equilateral triangle the length of its median being 9 units. Then the equation of that circle is

362.

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola   at the point (x1, y1). Then  is equal to :

• 10

• 5

• 8

• 6

#### Short Answer Type

363.

The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is ....

#### Multiple Choice Questions

364.

For some , if the eccentricity of the hyperbola,  is 5 times the eccentricity of the ellipse , , then the length of the latus rectum of the ellipse, is

• $\frac{2\sqrt{5}}{3}$

• $2\sqrt{6}$

• $\frac{4\sqrt{5}}{3}$

• $\sqrt{30}$

365.

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola is

• $64\sqrt{3}$

• $192\sqrt{3}$

• $128\sqrt{3}$

• $256\sqrt{3}$

366.

• None of these

367.

Let e1 and e2 be the eccentricities of the ellipse, respectively satisfying e1e= 1. If  are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair  is equal to:

• (8, 10)

• (8, 12)

#### Short Answer Type

368.

If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is.....

#### Multiple Choice Questions

369.

Let P(3, 3) be a point on the hyperbola, . If the normal to it at P intersects the x-axis at (9,0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :

370.

Let  be agiven ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function  then a+ b2 is equal to

• 145

• 126

• 116

• 135