Question

 

If C is the centre and A, B are two points on the conic

4x2 + 9y2 – 8x – 36y + 4 = 0 such that ∠ACB = π/2 then CA–2 +CB–2 is equal to  

Solution

Correct option is

 

We have, 

      

   

Clearly, the coordinates of C are (1, 2). 

Suppose CA makes an angle θ with the major axis. 

Then, the coordinates of A and B are 

      

          

          

Since A and B lie on (i). Therefore,  

       

and, 

       

and, 

          

SIMILAR QUESTIONS

Q1

The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrices is 18, is

Q2

The line x = at2 meets the ellipse  in the real points iff

Q3

On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y are

Q4

Tangent is drawn to the ellipse  , then the value of θ such that sum of intercepts on axes made by the tangent is minimum is  

Q5

If p and p’ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then     

Q6

If circumcentre of an equilateral triangle inscribed in  with vertices having eccentric angle α, β, γ respectively is (x1y1) then 

Q7

Locus of the middle points of all chords of , which are at a distance of 2 units from the vertex of parabola y2 = –8axis

Q8

A point on the ellipse  at a distance equal to the mean of lengths of the semi-major and semi-minor axis from the centre, is

Q9

A tangent to the ellipse  is cut by the tangent at the extremities of the major axis at T and T’. The circle on TT’ as diameter passes through the point

Q10

Ellipses which are drawn with the same two perpendicular lines as axes and with the sum of the reciprocals of squares of the lengths of their semi-major axis and semi-minor axis equal to a constant have only.