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.

find the area of the quadrilateral formed by a pair of tangents from the point (4,5) to the circle x^2 + y^2 -4x -2y-11 = 0 and pair of its radii.

Transverse common tangents are drawn from O to the two circles C_1,C_2 with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles C_1 and C_2 and chord of contacts of O w.r.t the circles C_1 and C_2 respectively is

The number of common tangents to the circles x^(2) + y^(2) = 4 and x^(2)+y^(2)-6x-8y=24 is

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

From the point (4,6) , a pair of tangent lines is drawn to the parabola y^2=8 x . The area of the triangle formed by these pairs of tangent lines and the chord of contact of the point (4,6) is

Equation of a common tangent to the circle x^(2) + y^(2) - 6x = 0 and the parabola, y^(2) = 4x , is

Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitrary point P on the line x+y =4 . The locus of mid-point of chord of contact AB is

A pair of tangents are drawn from the origin to the circle x^2 + y^2 + 20x +20y + 20 = 0 , The equation of pair of tangent is

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x^2+y^2=9 and the line joining their points of contact.