Circle

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

If an equilateral triangle is inscribed in the circle $4\left(x^2+y^2\right)+8(2x-y)+19=0,$ then length of the side is 

The centre of the circle $2x^2+2y^2-6x+4y+2=0$ is 

The centre and radius of the circle $x^2+{\left(y+2\right)}^2=0$ is 

A circle of area $9\pi \mathrm{square} \mathrm{units}$ has two of its diameters along the lines $x+y=5 \text{and} x-y=1$. Then the equation of the circle is 

The equation of the circle with centre $\left(2, 3\right)$ and passing through the intersection of the lines $3x-2y-1=0 \text{and} 4x+y-27=0$ is $x^2+y^2-4x-6y+k=0$, then find $k$.

The equation of the circle with centre $\left(2,-1\right)$ and passing through the point $\left(3, 6\right)$ is $(x-2{)}^2+(y+1{)}^2=k$, then find $k$.

The equation of the circles with radius $5 \mathrm{cm}$ and touching x-axis at the origin is 

The equation of the circle whose centre is $\left(1,1\right)$ and radius $\sqrt{2}$ is 

If the equation of the circle whose centre is at the origin and the radius is $5$ units is $x^2+y^2=k$, then find $k$.

If the equation of the circle passing through the origin and having the centre at $\left(-4,-3\right)$ is $x^2+y^2+ax+by=0$, then find $a+b$.

The equation of circle with centre $C$ and radius $r$ where $C=(-1,2), r=5$ is 

If the equation of a circle whose two diameters lie along the lines $2x-3y+12=0 \mathrm{and} x+4y-5=0$ and has area $154$ square units is $x^2+y^2+6x-4y+P=0$, then find the value of $P$.

If the equation of the circle whose centre is $\left(\frac{1}{2},\frac{1}{4}\right)$ and radius $\frac{1}{12}$ is $36x^2+36y^2-36x-Py+11$, then find the value of $P$.

The equation of the circle whose centre is $\left(0,2\right)$ and radius $2$ is 

If the equation of a circle whose centre is $\left(8,-6\right)$ and which passes through the point $\left(5,-2\right)$ is $x^2+y^2-16x+12y+k=0$, then find the value of $k$.

The equation of the circle with center $\left(2,2\right)$ which passes through $\left(4,5\right)$ is

If $x^2+y^2-5x-14y-34=0, x^2+y^2+2x+4y+k=0$ circles are orthogonal then find ${}^{\text{'}}k^{\text{'}}$.

Find the equation of the circle passing through the points $(9,1),(7,9),(-2,12)$ Does the point $\left(6,0\right)$ lie on the circle, answer yes or no.