Tangents drawn from the point `P(1,8)` to the circle `x^2 +y^2 -6x -4y-11=0` touch the circle at the points A&B ifR is the radius of circum circle of triangle PAB then [R]-

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.

Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it at the point A in the first quadrant. Find the coordinates of another point B on the circle such that A B=4 .

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

Tangents are drawn from external point P(6,8) to the circle x^2+y^2 =r^2 find the radius r of the circle such that area of triangle formed by the tangents and chord of contact is maximum is (A) 25 (B) 15 (C) 5 (D) none of these

lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-6y-12 = 0 externally at a point (1, -1), then the radius of the circle C is :-

Find the points on the circle x^2+y^2-2x+4y-20=0 which are the farthest and nearest to the point (-5,6)dot

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then find the radius of the circle.

If the chord of contact of the tangents drawn from a point on the circle x^2+y^2=a^2 to the circle x^2+y^2=b^2 touches the circle x^2+y^2=c^2 , then prove that a ,b and c are in GP.

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 is circle with radius

The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = 8x touch the circle at P,Q andthe parabola at R,S . Then area of quadrilateral PQRS is