## Question

### Solution

Correct option is The given ellipse is inscribed in a rectangle PQRS as shown in figure. Clearly, coordinates of P are (2, 1). The rectangle PQRSis inscribed in another ellipse passing through (4, 0). So, its semi-major axis is 4.

Let the equation of the ellipse where a = 4. This passes through (2, 1).   Hence, the equation of ellipse is  .

#### SIMILAR QUESTIONS

Q1

If α and β are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

Q2 , then the chord joining two points θ1 and θ2 on the ellipse will subtend a right angle at

Q3

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is a/an

Q4

The number of values of c such that the straight line y = 4x + ctouches the curve , is

Q5 , then PF1 + PF2 equals

Q6

An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an

Q7

The sum of the squares of the perpendicular on any tangent to the ellipse from two points on the minor axis, each at a distance from the centre is

Q8

The eccentric angle of a point on the ellipse whose distance from the centre of the ellipse is 2, is

Q9

If any tangent to the ellipse intercepts equal length lon the axes, then =

Q10

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is