The Area Of The Parallelogram Formed By Tangents At The Extremities Of Two Conjugate Diameters Of The Ellipse  is Equal To

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 3x² + 2y² = 5 is

The ellipse  cuts x-axis at A and A’ and y-axis at Band B’. The line joining the focus S and B makes an angle  with x-axis. The eccentricity of the ellipse is

A circle is drawn on the major axis of the ellipse 9x² + 16y² = 144 as diameter. The equation of circle is

The equation  represents an ellipse, if

S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is 

The locus of mid-points of focal chords of the ellipse  is 

If  touches the ellipse , then its eccentricity angle θ is equal to

If the polar with respect to the parabola y² = 4ax touches the ellipse , then the locus of its pole is  

The locus of mid-point of the portions of the tangents to the ellipse  included between the axes is the curve 

If the angle between the straight lines joining foci and the ends of minor axis of the ellipse  is 90⁰ then the eccentricity is