Ellipse PYQs - Last 10 Years

The tangent and normal to the ellipse 3x2
+ 5y2
= 32 at the point P(2, 2) meet the x-axis at Q and R,
respectively. Then the area (in sq. units) of the triangle PQR is :

If the length of the latus rectum of an ellipse is 4 units and the distance between a focus an its nearest vertex on the major axis is \({3 \over 2}\) units, then its eccentricity is :

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate
axes and passing through the points (4, −1) and (−2, 2) is :

Consider an ellipse, whose center is at the origin and its major axis is along the x-axis. If its eccentricity is \({3 \over 5}\) and the distance between its foci is 6, then the area (in sq. units) of the quadrilatateral inscribed in the e...

The eccentricity of an ellipse whose centre is at the origin is \({1 \over 2}\). If one of its directrices is x = – 4, then the
equation of the normal to it at \(\left( {1,{3 \over 2}} \right)\) is :