Tangents are drawn to the circles `x^(2)+y^(2)+4x+6y-19=0,x^(2)+y^(2)=9` from any point on the 2x+3y=5. Prove that their lengths are equal.

The pair of tangents from origin to the circle x^(2)+y^(2)+4x+2y+3=0 is

If a point P is moving such that the lengths of the tangents drawn form P to the circles x^(2) + y^(2) + 8x + 12y + 15 = 0 and x^(2) + y^(2) - 4 x - 6y - 12 = 0 are equal then find the equation of the locus of P

From a point P , tangents drawn to the circle x^2 + y^2 + x-3=0, 3x^2 + 3y^2 - 5x+3y=0 and 4x^2 + 4y^2 + 8x+7y+9=0 are of equal lengths. Find the equation of the circle through P , which touches the line x+y=5 at the point (6, -1) .

If a point P is moving such that the lengths of tangents drawn from P to the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+6x+18y+26=0 are the ratio 2:3, then find the equation to the locus of P.

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that

The length of the tangent to the circle x^(2)+y^(2)-2x-y-7=0 from (-1, -3), is

If two tangents are drawn from a point to the circle x^(2) + y^(2) =32 to the circle x^(2) + y^(2) = 16 , then the angle between the tangents is

If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles x^(2)+y^(2)+2x-4y-20=0 and x^(2)+y^(2)-4x+2y-44=0 is 2:3, then the locus of P is a circle with centre .

Tangents are drawn from a point on the circle x^(2)+y^(2)-4x+6y-37=0 to the circle x^(2)+y^(2)-4x+6y-12=0 . The angle between the tangents, is