From a point 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=0 is

The equations of the two common tangents to the circle x^(2) +y^(2)=2a^(2) and the parabola y^(2)=8ax are-

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

Find the equation of the common tangents to y^2 - 8ax and x^2 + y^2 = 2a^2

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

If the length of the common chord of circle x^2+y^2=4 and y^2=4(x-h) is maximum, then find the value of h .

The number of common tangent to two circle x ^(2) +y^(2) =4 and x^(2) +y^(2) -8x+12=0 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.