If `S-=x^2+y^2-4x=0, S'-=x^2+y^2+8x=0` and AB is a direct common tangent to the two circles where A,B are points of contact then find the angle subtended by AB at origin.

Find the common tangent of y=1+x^(2) and x^(2)+y-1=0 . Also find their point of contact.

Tangents are drawn from any point on the line x+4a=0 to the parabola y^2=4a xdot Then find the angle subtended by the chord of contact at the vertex.

Tangents are drawn from any point on the line x+4a=0 to the parabola y^2=4a xdot Then find the angle subtended by the chord of contact at the vertex.

y=3x is tangent to the parabola 2y=ax^2+ab . If b=36,then the point of contact is

Find the equation of the common tangent of the following circles at their point of contact. x^2+y^2-8y-4=0 x^2+y^2-2x-4y=0

The common tangent at the point of contact of the two circles x^2+y^2-4x-4y=0, x^2+y^2+2x+2y=0 is

Consider two circles S, =x^2+y^2 +8x=0 and S_2=x^2+y^2-2x=0 . Let DeltaPOR be formed by the common tangents to circles S_1 and S_2 , Then which of the following hold(s) good?

Find the equation of the circle passing through the points of contact of the direct common tangent of x^2+y^2=16 and x^2+y^2-12x+32=0

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

The number of common tangents to the circles x^2+y^2-x = 0 and x^2 + y^2 + x = 0 are