`P(a,5a)` and `Q(4a,a)` are two points. Two circles are drawn through these points touching the axis of y.
Centre of these circles are at

How many circles can be drawn through " two points " ?

Let P(alpha,beta) be a point in the first quadrant. Circles are drawn through P touching the coordinate axes. Radius of one of the circles is

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

Centre of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2 is

Variable circles are drawn touching two fixed circles externally then locus of centre of variable circle is

A variable circle passes through the fixed point (2,0) and touches y-axis then the locus of its centre 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.