The eccentricity of the ellipse with centre at the origin which meets the straight line on the axis of x and the straight line on the axis of y and whose axes lie along the axes of coordinates is
None of these
Let the equation of the ellipse be .
It cuts the coordinate axes at (7, 0) and (0, –5).
On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y 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 (x1, y1) then
Locus of the middle points of all chords of , which are at a distance of 2 units from the vertex of parabola y2 = –8axis
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
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
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.
The radius of the circle passing through the foci of the ellipse
9x2 + 16y2 = 144 and having its centre at (0, 3), is