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Revision Quiz on Ellipse and Hyperbola

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Question 1

The eccentricity of the ellipse

Question 2

If the line

intersects the ellipse

.Find angle at origin subtended by them.

Question 3

Find the ellipse passing through midpoint of focus on positive axis and vertex on opposite side of

and through (0.1,0.1) and its centre is same as given ellipse.

Question 4

The equation of the ellipse, whose focus is the point (–1, 1), whose directrix is the straight line x – y + 3 = 0 and whose eccentricity is 1/2 is:

Question 5

The equation of tangents to the ellipse

which are inclined at 30⁰ to the x-axis, are

Question 6

Lines x + y = 1 and 3y = x + 3 intersect the ellipse x² + 9y² = 9 at the points P, Q R. The area of the triangle PQR is

Question 7

A point (x,y) on ellipse is defined by

.If distance of one focus from the point is 5, find distance of the point from another focus.

Question 8

The equation of the hyperbola with Foci

the conjugate axis is of length 24

Question 9

If the focil of $Description: E:\KCET-1-Feb\KARNATAKA-CET-2011_files\image486.png$ = 1 and $Description: E:\KCET-1-Feb\KARNATAKA-CET-2011_files\image487.png$ = 1coincide, then value of a is

Question 10

If PQ is a double ordinate of hyperbola

. Such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then the eccentricity 'e' of the hyperbola satisifes

Question 11

The equation of tangents to the hyperbola 3x² – 2y² = 6, which is perpendicular to line x – 3y = 3, are

Question 12

The length of transverse axis of the rectangular hyperbola xy = 18 is

Question 13

Conic sections are broadly classified into 3 types Parabola, ellipse and hyperbola. Based on this find the equation to the hyperbola whose asymptotes are the straight lines x+3y-1=0 and 2x-y+7=0 and which passes through the point (1,2).

Question 14

The equation of the hyperbola with Foci

passing through (2, 3)

Question 15

Find the equation of a hyperbola with foci at (-2 , 0) and (2 , 0) and asymptotes given by the equation y = x and y = -x

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Feb 12JEE & BITSAT