Two circles are drawn through the points `(a,5a) and (4a, a)` to touch the y-axis. Prove that they intersect at angle `tan^-1(40/9).`

Equation of circles which pass through the point (1,-2) and (3,-4) and touch the x- axis is

The circle passing through the point (-1,0) and touching the y -axis at (0,2) also passes through the point:

The circles which can be drawn to pass through (3,0) and (5,0) and to touch the y-axis intersect at an angle theta , then costheta is equal to

The circle which can be drawn to pass through (1,0) and (3,0) and to touch the y-axis intersect at angle theta. Then cos theta is equal to (1)/(2) (b) -(1)/(2)( c) (1)/(4)(d)-(1)/(4)

A circle passes through the points (2, 2) and (9, 9) and touches the x-axis. The absolute value of the difference of possible x-coordinate of the point of contact is______.

the equation of the circle passing through the point (2,1) and touching y -axis at the origin is

Find the equation of the circle passing through the points A(4,3).B(2,5) and touching the axis of y.Also find the point P on the y-axis such that the angle APB has largest magnitude.