The tangent at any point on the ellipse meets the tangents at the vertices A, A' in L and L'. Then AL. A'L' =

The circle on SS' as diameter intersects the ellipse in real points then its eccentricity (where S and S'are the focus of the ellipse)

The circle on SS'as diameter touches the ellipse then the eccentricity of the ellipse is (where S and S'are the focus of the ellipse)

The tangent at P on the ellipse meets the minor axis in Q, and PR is drawn perpendicular to the minor axis and C is the centre. Then CQ . CR =

If P is a point on the ellipse of eccentricity e and A, A' are the vertices and S, S' are the focii then ΔSPS' : ΔAPA'=

If the latus rectum of the ellipse x² tan²  + y² sec² = 1 is then  =

LL' is the latus rectum of an ellipse and ΔSLL' is an equilateral triangle. The eccentricity of the ellipse is -

The common tangent of x² + y² = 4 and 2x² + y² = 2 is-

Eccentric angle of a point on the ellipse x² + 3y² = 6 at a distance 2 units from the centre of the ellipse is -

The sum of the squares of the perpendicular on any tangent to the ellipse + = 1 from two points on the minor axis each distance from the centre is -

Let E be the ellipse + = 1 and C be the circle x² + y² = 9. Let P and Q be the points (1, 2) and (2, 1) respectively. Then -

The area of quadrilateral formed by tangents at the ends of latus-rectum of the ellipse x² + 2y² = 2 is-

the tangents are symmetrical about the origin. hence, the area of one of the triangles can be multiplied by 4 to get the total area.

The locus of mid-points of a focal chord of the ellipse = 1 is-

the equation of chord with a given midpoint is:
xx₁/a²+yy₁/b²=x₁²/a²+y₁²/b²
where (x1,y1) is the midpoint.

The equation of the chord of the ellipse 2x² + 5y² = 20 which is bisected at the point (2,1) is-

The locus of the point of intersection of the perpendicular tangents to the ellipse + = 1 is

perpendicular tangents are drawn from the director circle

From the point (, 3) tangents are drawn to + = 1 and are perpendicular to each other then  =

perpendicular tangents are drawn from the director circle