The equation of the line through the origin which cuts the circle `x^2 + y^2- 4x-2y- 20=0` at the points A an B such that `AB = 4sqrt5`, is

The equation of the circle radius is 5 and which touches the circle x^(2)+y^(2)-2x-4y-20=0" at this point (5,5) is"

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The equation of a line which makes concentric to the circle x^2+y^2-4x+2y-20=0 and passes through the origin is __

The equation of the circle concentric with the circle x ^(2) + y^(2) -4x-6y =0 and passing through the point (-4,-5) is

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and the lines xy -2x -y+2=0 orthogonally, is

Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and the lines xy -2x -y+2=0 orthogonally, is

The equation of the circle passing through the points of intersection of the circle x^(2)+y^(2)-2x+4y-20=0 , the line 4x-3y-10 =0 and the point (3, 1) is