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

An equation of a line passing through the point (-2, 11) and touching the circle x^(2) + y^(2) = 25 is

Show that the equation of a line passing through the point (11,-2) and touching the circle x^(2)+y^(2)=25 is 3x+4y=25 .

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

If the radius of the circle passing through the origin and touching the line x+y=2 at (1, 1) is r units, then the value of 3sqrt2r is

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

A circle passes through the point (3, 4) and cuts the circle x^2+y^2=c^2 orthogonally, the locus of its centre is a straight line. If the distance of this straight line from the origin is 25. then a^2=

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

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