Question

The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

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