The locus of extremities of the latus rectum of the family of ellipses b²x² + y² = a²b² is

If A, A' are the vertices S, S' are the focii and Z, Z' are the feet of the directrix of an ellipse then A'S, A'A, A'Z are in

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 lines parallel to the y axis are pf the form x=a since the y intercept is undefined.

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-