Question

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is

Solution

Correct option is

 

The equation of the tangent at P(θ) to the ellipse 

        

The combined equation of the lines CQ and CR is      

        

The lines represented by this equation are at right angle. 

.  

SIMILAR QUESTIONS

Q1

If S and S’ are two focii of the ellipse 16x2 + 25y2 = 400 andPSQ is a focal chord such that SP = 16, then SQ = 

Q2

Tangent at a point on the ellipse  is drawn which cuts the coordinates axes at A and B. The minimum area of the triangleOAB is (O being origin)

Q3

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse 

Q4

The locus of the point of intersection of tangents to the ellipse  at the points whose eccentric angles differ by  is  

Q5

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

Q6

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

Q7

, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are 

Q8

The locus of the point of intersection of perpendicular tangents to.

Q9

S(3, 4) and S’(9, 12) are two foci of an ellipse. If the foot of the perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then the eccentricity of the ellipse is  

Q10

Let d1 and d2 be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse  to the tangent at any point P on the ellipse. Then, SP : SP’ =