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.

If tangents are drawn from origin to the circle x^(2)+y^(2)-2x-4y+4=0, then

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) .

Find the radical center of the circles x^(2)+y^(2)+4x+6y=19,x^(2)+y^(2)=9,x^(2)+y^(2)-2x-4y=5

Length of tangent from (8,6) to the circle x^(2)+y^(2)-3x-4y+2=0

The lengths of the common tangents of the circles x^(2)+y^(2)+4x=0 and x^(2)+y^(2)-6x=0 is

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

If the tangent at the point on the circle x^(2)+y^(2)+6x+6y=2 meets the straight ine 5x-2y+6=0 at a point Q on the y -axis then the length of PQ is

Tangents drawn from the point (4, 3) to the circle x^(2)+y^(2)-2x-4y=0 are inclined at an angle