Question
An ellipse has OB as a semiminor axis, F, F’ as its foci and the angle ∠FBF’ is a right angle. Then, the eccentricity of the ellipse is


None of these


easy
Solution
We have,
.
SIMILAR QUESTIONS
If p and p’ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semimajor 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} = –8axis
A point on the ellipse at a distance equal to the mean of lengths of the semimajor and semiminor 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
4x^{2} + 9y^{2} – 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 semimajor axis and semiminor axis equal to a constant have only.
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
The radius of the circle passing through the foci of the ellipse
9x^{2} + 16y^{2} = 144 and having its centre at (0, 3), is
The focus of an ellipse is (–1, –1) and the corresponding directix is x – y + 3 = 0. If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse are