P is a variable point on the ellipse += 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor

A man running round a race course, notes that the sum of the distances of two flag-posts from him is always 10 meters and the distance between the flag- posts is 8 meters. The area of the path he encloses in square metres is-

If C is the centre of the ellipse 9x² + 16y² = 144 and S is one focus. The ratio of CS to major axis, is

If any tangent to the ellipse intercepts equal lengths  on the axes, then  =

The line x = at² meets the ellipse in the real points if

The length of the common chord of the ellipse and the circle (x –1)² + (y –2)² = 1 is

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-