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
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
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
, then the chord joining two points θ1 and θ2 on the ellipse will subtend a right angle at
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
The number of values of c such that the straight line y = 4x + ctouches the curve , is
, then PF1 + PF2 equals
An ellipse slides between two perpendicular straight lines. Then, the locus of its centre is a/an
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
The eccentric angle of a point on the ellipse whose distance from the centre of the ellipse is 2, is
If any tangent to the ellipse intercepts equal length lon the axes, then l =
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