## Question

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

4*x*^{2} + 9*y*^{2} – 8*x* – 36*y* + 4 = 0 such that ∠*ACB* = π/2 then *CA*^{–2} +*CB*^{–2} is equal to

### Solution

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

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

The line *x* = *at*^{2} meets the ellipse in the real points iff

On the ellipse 4*x*^{2} + 9*y*^{2} = 1, the points at which the tangents are parallel to the line 8*x* = 9*y* are

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

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

If circumcentre of an equilateral triangle inscribed in with vertices having eccentric angle α, β, γ respectively is (*x*_{1}, *y*_{1}) then

Locus of the middle points of all chords of , which are at a distance of 2 units from the vertex of parabola *y*^{2} = –8*ax*is

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

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

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.