R D Sharma Solutions for Chapter: Ellipse, Exercise 1: EXERCISE 26.1

Find the equation of the ellipse in the following cases:

eccentricity $e=\frac{1}{2}$ and semi-major axis $=4$

Find the equation of the ellipse in the following cases:

eccentricity $e=\frac{1}{2}$ and major axis $=12$

Find the equation of the ellipse in the following cases:

Vertices $(\pm 5,0),$ foci $(\pm 4,0)$

Find the equation of the ellipse in the following cases:

Ends of major axis $(\pm 3,0),$ ends of minor axis $(0,\pm 2)$

Find the equation of the ellipse in the following cases:

Length of minor axis $16$ and foci $(0, \pm 6)$

Find the equation of the ellipse in the following cases:

$Foci(\pm 3,0), a=4$

Find the equation of the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is $10$

Find the eccentricity of an ellipse whose latus-rectum is half of its minor axis