Family of Circles

Find the equation of a circle which passes through the point $(1, 2)$ and the points of intersection of the circles $x^2+y^2-8x-6y+21=0$ and $x^2+y^2-2x-15=0.$

A circle $c$ passing through the point $\left(6,2+2\sqrt{3}\right)$ touches the circle $x^2+y^2-2x-4y-4=0$ externally at the point $\left(4,2\right)$, then diameter of circle $c$ is

If $x+y=3$ is the equation of the chord $AB$ of the circle $x^2+y^2-2x+4y-8=0$, then the equation of the circle having $AB$ as diameter is

Center of the circle which passes through the point $\left(-2,2\right)$ and touches the circle $x^2+y^2-6x+8y=0$ at the point $\left(0,0\right)$ will be

The radius of the circle touching the line $\mathrm{x}+\mathrm{y}=4$ at $\left(\mathrm{1,3}\right)$ and intersecting ${\mathrm{x}}^2+{\mathrm{y}}^2=4$ orthogonally is

If the diameter of first circle is the common chord for other circles having equation $x^2+y^2+2x+3y+1=0$ and $x^2+y^2+4x+3y+2=0$, then find the equation of first circle

Find the equation of the circle whose center lies on $3x+4y=7$ and which passes through the points $(1, -2)$ and $(4, -3)$.

If the circle $x^2+y^2+6x+8y-5=0$ is concentric with the circle $x^2+y^2+2gx+2fy+c=0$ on which the point $(-3, 2)$ lies, then the value of $c$ will be:

The coordinates of the two fixed points through which the circle $x^2+y^2-2x+\lambda x-1=0$ passes are

The equation to the circle which touches the axis of $y$ at the origin and passes through $\left(3, 4\right)$ is

The equation of the circles passing through $\left(1, 2\right)$ and the points of intersection of the circles $x^2+y^2-8x-6y+21=0$ and $x^2+y^2-2x-15=0$ is

If $x-y+1=0$ meets the circle $x^2+y^2+y-1=0$ at A and B then the equation of the circle with AB as diameter is

Find the equation of the circle through the point $\left(-2, 4\right)$ and through the points of intersection of the circle $x^2+y^2+2x-4y-4=0$ and the line $3x+2y-5=0$

Equation of smallest circle passing through 'points of intersection of line $x+y=1$ & circle $x^2+y^2=9$

The $P$ be the family of parabolas $y=x^2+px+q \left(q \ne 0\right)$ whose graphs cut the axes in three points. The family of circles through these three points have a common point

The equation of the circle whose diameter is the common chord of the circles ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}+3\mathrm{y}+2=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2+2\mathrm{x}-3\mathrm{y}-\mathrm{ }4=0$ is-

A triangle is formed by the lines whose combined equation given by $\left(x+y- 4\right)\left(xy- 2x- y+2\right)= 0$. The equation of circumcircle is -

The circle ${\mathrm{x}}^2+{\mathrm{y}}^2=1$ is completely contained in the circle ${\mathrm{x}}^2+{\mathrm{y}}^2+4\mathrm{x}+3\mathrm{y}+\mathrm{k}=0$ , if

The circle whose diameter is the chord $\mathrm{x}+\mathrm{y}=1$ of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=4$ is

The intercept on the line $y=x$ by the circle $x^2+y^2-2x=0$ is $AB\mathit{.}$ Equation of circle with $AB$ as diameter is-