Conic Sections Quiz for JEE & BITSAT Exams

Question 1

Let P be the point on the parabola, y²= 8x which is at a minimum distance from the centre C of the circle, x² + (y + 6)² = 1. Then the equation of the circle, passing through C and having its centre at P is

Question 2

The radius of a circle, having the minimum area, which touches the curve y=4−x² at vertex and the lines, y=|x| is

Question 3

The slope of the line touching both the parabolas y² = 4x and x² = – 32y is

Question 4

A tangent is drawn to the parabola y = x² + 6 at the point (1, 7) which also touches the circle
x² + y² + 16x + 12y + c = 0 at

Question 5

Angle between tangents drawn from the point (1, 4) to the parabola y² = 4x is

Question 6

Equation of common tangent of y = x², y = –x² + 4x –4 is:

Question 7

Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is NOT given by

Question 8

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its focii, is

Question 9

The equation of the circle passing through the foci of the ellipse

and having center at (0, 3) is:

Question 10

If e₁ is the eccentricity of the ellipse and

e₂ is the eccentricity of the hyperbola passing through the foci of the ellipse and e₁e₂ = 1, then equation of the hyperbola is:

Question 11

If a hyperbola passes through the point

and has foci at

. Then the tangent to this hyperbola at P also passes through the point:

Question 12

The eccentricity of an ellipse whose centre is at the origin is 1/2, If one of its directrix is x=−4, then the equation of the normal to it at (1, 3/2) is:

Question 13

The area (in sq. units) of the quadrilateral formed by the tangents at the points of the latera recta to the ellipse

= 1, is

Question 14

The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it is

Question 15

Tangents are drawn to the hyperbola 4x² - y² = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of ΔPTQ is :