If α – β = constant, then the locus of the point of intersection of tangents at to the ellipse
Let R(h, k) be the point of intersection of tangents at P and Q. Then,
Hence, the locus of R(h, k) is
Clearly, it represents an ellipse.
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 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
9x2 + 16y2 = 144 and having its centre at (0, 3), is
An ellipse has OB as a semi-minor axis, F, F’ as its foci and the angle ∠FBF’ is a right angle. Then, the eccentricity of the ellipse 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
The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through (4, 6) is
Tangents are drawn to the ellipse and the circle x2 + y2 = a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then, the greatest acute angle between these tangents is given by
The area of the quadrilateral formed by the tangents at the end-points of latusrecta to the ellipse
Let S(3, 4) and S’(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is