Circle

The equation of a circle which touches the straight lines $x+y=2, x-y=2$ and also touches the circle $x^2+y^2=1$ is

If $S \equiv 2 x^2+2 y^2-8 x+8 y-7=0$ is the circle passing through the points of intersection of the circles $x^2+y^2+$ $\mathrm{kx}-\mathrm{ky}+1=0$ and $\mathrm{x}^2+\mathrm{y}^2-\mathrm{kx}+\mathrm{ky}-2=0$, then…

If the mid point of the chord intercepted by the circle $x^2+y^2-8 x+10 y+5=0$ on the line $2 x+y+2=0$ is $(\mathrm{h}, \mathrm{k})$, then $\mathrm{k}+4 \mathrm{~h}=$

The product of the slopes of the common tangents drawn to the circles $x^2+y^2+2 x-2 y-2=0$ and $x^2+y^2-2 x+$

The triangle $P Q R$ is inscribed in the circle $x^2+y^2=25$. If $\mathrm{Q}=(3,4)$ and $\mathrm{R}=(-4,3)$ then $\angle \mathrm{QPR}=$

If $Q$ is the inverse point of the point $\mathrm{P}(2,3)$ with respect to the circle $x^2+y^2-2 x-2 y+1=0$, then the circle with $\mathrm{PQ}$ as diameter is

If the lines joining the origin to the points of intersection of a line $\mathrm{L}$ and $\mathrm{x}^2+\mathrm{y}^2=4$ are the coordinate axes, then the equation of the line $\mathrm{L}$ is

$2 x-3 y+1=0$ and $4 x-5 y-1=0$ are the equations of two diameters of the circle $S \equiv x^2+y^2+2 g x+2 f y-11=0$. Q and R are the points of contact of the tangents drawn from the point $P(-2,-2)$ to this circle. If…

If $2 x-3 y+3=0$ and $x+2 y+k=0$ are conjugate lines with respect to the circle $\mathrm{S} \equiv x^2+y^2+8 x-6 y-24=0$, then the length of the tangent drawn from the point $\left(\frac{k}{4}, \frac{k}{3}\right)$ to…

If the length of the chord $2 x+3 y+k=0$ of the circle $x^2+y^2-6 x-8 y+9=0$ is $2 \sqrt{3}$, then one of the values of $\mathrm{k}$ is

If the equation of the circle of radius 3 units which touches the circle $x^2+y^2+6 x-8 y-11=0$ externally at $(3,0)$ is $x^2+y^2+2 g x+2 f y+c=0$, then $3 g-4 f+c=$

If the lines $2 x+y+12=0, k x-3 y-10=0$ are conjugate with respect to the circle $x^2+y^2-4 x+3 y-1=0$, then $k=$