The Slope Of A Common Tangent To The Ellipse  and aconcentric Circle Of Radius r is

The sum of the squares of the perpendicular on any tangent to the ellipse  from two points on the minor axis, each at a distance  from the centre is 

The eccentric angle of a point on the ellipse  whose distance from the centre of the ellipse is 2, is

If any tangent to the ellipse  intercepts equal length lon the axes, then l =

The ellipse x² + 4y² = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is  

A focus of an ellipse is at the origin. The directrix is the line  x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis, is  

In an ellipse, the distance between its foci is 6 and minor axis is 8. The eccentricity is 

The tangent at a point  meets the auxiliany circle in two points. The chord joining them subtends a right angle at the centre. Then, the eccentricity of the ellipse is given by  

If F₁ and F₂ be the feet of the perpendicular from the foci S₁and S₂ of an ellipse  on the tangent at any point P on the ellipse, then (S₁F₁)(S₂F₂) is equal to   

The area of the rectangle formed by the perpendiculars from the centre of the ellipse to the tangent and normal at the point-whose eccentric angle is , is  

P is a variable point on the ellipse  with AA’ as the major axis. Then, the maximum value of the area of the triangleAPA’ is