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.

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. (-1/2,1/2) (b) (1, 1) (1/2,1/2) (d) none of these

lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-6y-12 = 0 externally at a point (1, -1), then the radius of the circle C 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) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

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

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

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

A curve passing through the origin has its slope. e^(x) . Find the equation of the curve.

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0 . Find its equation if its axes coincide with the coordinate axes.

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0 . Find its equation if its axes coincide with the coordinate axes.