Show that the area of the quadrilateral formed by the common tangents to the circle `x^2 +y^2=c^2` an the ellipse `x^2/a^2 +y^2/b^2=1 , b < c < a` is `(2c^2(a^2-b^2))/sqrt((a^2-c^2)*(c^2-b^2))`

A common tangent to the circle x^(2) +y^(2) =16 and an ellipse (x^(2) )/( 49) +(y^(2))/( 4) = 1 is

The area of the quadrilateral formed by the tangents at the end points of latus rectum of the ellipse 5x^(2) +9y^(2)=45 is

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse (x^(2))/(9)+(y^(2))/(5)=1 is

The equation of a common tangent to the circle x^(2)+y^(2)=16 and the ellipse (x^(2))/(49)+(y^(2))/(4)=1 is

The locus of the poles of tangents to the auxiliary circle with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

The locus of the poles of tangents to the auxiliary circle with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Area of quadrilateral formed by direct common tangents to circles x^(2)+y^(2)-6x=0,x^(2)+y^(2)+2x=0& their chord of contacts is

From a pt A common tangents are drawn to a circle x^(2)+y^(2)=(a^(2))/(2) and y^(2)=4ax. Find the area of the quadrilateral formed by common tangents,chord of contact of circle and chord of contact of parabola.

From a pt A common tangents are drawn to a circle x^2 +y^2 = a^2/2 and y^2 = 4ax . Find the area of the quadrilateral formed by common tangents, chord of contact of circle and chord of contact of parabola.