Question

Solution

Correct option is Let the equation of the ellipse be It passes through (4, 6). Let e be the eccentricity of the ellipse. Then,

ae = Distance between (1, 2) and (6, 2)    Solving (ii) and (iii), we get a2 = 45, and b2 = 20

Hence, the equation of the ellipse is, .

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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.

Q6

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

Q7

The radius of the circle passing through the foci of the ellipse

9x2 + 16y2 = 144 and having its centre at (0, 3), is

Q8

An ellipse has OB as a semi-minor axis, FF’ as its foci and the angle FBF’ is a right angle. Then, the eccentricity of the ellipse is

Q9

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

Q10

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