Equation of Circle

Tangents drawn from the point $P(1, 8)$ to the circle 

$x^2+y^2-6x-4y-11=0$

touch the circle at the points $A$ and $B$. The equation of the circumcircle of the triangle $PAB$ is

Extremities of a diagonal of a rectangle are $\left(0, 0\right)$ and $\left(4, 3\right).$ Find the equation of the tangents to the circumcircle of a rectangle which are parallel to this diagonal.

The circle $C: x^2+y^2+kx+\left(1+k\right)y-\left(k+1\right)=0$ passes through two fixed points for every real number $K$. The minimum value of the radius of circle $C$ is

If $A$ and $B$ are fixed points in the plane such that $\frac{PA}{PB}=k$  (constant) for all $P$ on a given circle, then the value of $k$ cannot be equal to:

The equation of a circle with centre on $y-$axis and passing through the origin and the point $(3, 4)$ is

The number of integer values of $k$ for which the equation $x^2+y^2+\left(k-1\right)x-ky+5=0$ represents a circle whose radius cannot exceed $3$, is

Let $C$ be the circle whose diameter is the line segment formed by the line $3x+2y=6$ intercepted by the coordinate axes. Then $C$ also passes through the point.

Consider a family of circles which are passing through the point $\left(-1,1\right)$ and are tangent to  $x-$axis. If $\left(h,k\right)$ are the coordinate of the centre of the circles, then the set of values of $k$ is given by the interval

If the abscissa and ordinates of two points $P$ and $Q$ are roots of the equations $x^2+2ax-b^2=0$ and $y^2+2py-q^2=0$ respectivaly, then the equation of the circle with $PQ$ as diameter, is

The other end of the diameter through the point $\left(-1, 1\right)$ on the circle $x^2+y^2-6x+4y-12=0$ is

The area of the circle $x^2-2x+y^2-10y+k=0$ is $25\pi .$ The value of $k$ is equal to

Centre of circle whose normals are $x^2-2xy-3x+6y=0$, is

Let $A\left(1,2\right), B\left(3,4\right)$ be two points and $C\left(x,y\right)$ be a point such that area of $∆ABC$ is $3$ sq. units and $\left(x-1\right)\left(x-3\right)+\left(y-2\right)\left(y-4\right)=0$. Then number of positions of $C$, in the$xy$ plane, is 

The equation of the circle concentric with the circle $x^2+y^2-6x-4y-12=0$ and touching $Y$-axis

If the equation $p{x}^2+\left(2-q\right)xy+3y^2-6qx+30y+6=0$ represents a circle, then the value of $p+q$.

The equation of the circle concentric with the circle $x^2+y^2-6x-4y-12=0$ and touching $Y$-axis

A circle passes through the points $\left(2,3\right)$ and $\left(4,5\right)$. If its centre lies on the line, $y-4x+3=0$, then its radius is equal to :

The equation of the circle of radius $3$ that lies in the fourth quadrant and touching the lines $x=0$ and $y=0$ is

The centre of the circle $x=2+3\cos \mathrm{\theta }, y=3\sin \theta -1$ is