Circle

Find the equation of the circle passing through \((1,-2)\) and touching the \(X\)-axis at \((3,0)\).

If the chord of contact of tangents from a point on the circle \(x^2+y^2=r_1^2\) to the circle \(x^2+y^2=r_2^2\) touches the circle \(x^2+y^2=r_3^2\), then \(r_1, r_2\) and \(r_3\) are in

Find the equations of the tangents drawn to the circle \(x^2+y^2=50\) at the points where the line \(x+7=0\) meets it.

The equation of the circle, which cuts orthogonally each of the three circles
$$\begin{aligned} & x^2+y^2-2 x+3 y-7=0, \\ & x^2+y^2+5 x-5 y+9=0 \text { and } \\ & x^2+y^2+7 x-9 y+29=0 \end{aligned}$$

The length of the tangent from any point on the circle \((x-3)^2+(y+2)^2=5 r^2\) to the circle \((x-3)^2+(y+2)^2=r^2\) is 16 units, then the area between the two circles in square units is

If a foot of the normal from the point \((4,3)\) to a circle is \((2,1)\) and \(2 x-y-2=0\), is a diameter of the circle, then the equation of circle is

Find the equation of a circle whose radius is 5 units and passes through two points on the \(X\)-axis, which are at a distance of 4 units from the origin

If \(P(-9,-1)\) is a point on the circle \(x^2+y^2+4 x+8 y-38=0\), then find equation of the tangent drawn at the other end of the diameter drawn through \(P\)

The equations of the tangents to the circle \(x^2+y^2=4\) drawn from the point \((4,0)\) are

Given, two fixed points \(A(-2,1)\) and \(B(3,0)\).
Find the locus of a point \(P\) which moves such that the angle \(\angle A P B\) is always a right angle.