If a line passing through the origin touches the circle `(x-4)^2+(y+5)^2=25` , then find its slope.

Find the circle of minimum radius which passes through the point (4, 3) and touches the circle x^2+y^2=4 externally.

If r_1 and r_2 are the radii of smallest and largest circles which passes through (5,6) and touches the circle (x-2)^2+y^2=4 , then r_1,r_2 is

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

A circle of radius 1 unit touches the positive x-axis and the positive y-axis at A and B , respectively. A variable line passing through the origin intersects the circle at two points D and E . If the area of triangle D E B is maximum when the slope of the line is m , then find the value of m^(-2)

The centre of a circle passing through the points (0,0),(1,0)and touching the circle x^2+y^2=9 is

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is

a circle passing through the point (2,2(sqrt2-1)) touches the pair of lines x^2 -y^2 -4x+4 =0 . The centre of the circle is

Find the equation of a straight line passing through the origin and through the point of intersection of the lines 5x + 7y =3 and 2x – 3y = 7

If a circle whose center is (1,-3) touches the line 3x-4y-5=0 , then find its radius.

Find the equation of the straight line which passes through the centre of the circle x^(2) + y^(2) + 2x + 2y- 23 = 0 and is perpendicular to the straight line x-y+8 = 0.