Circle

The equation to two circles which touch the $Y$-axis at $(0,3)$ and make an intercept of 8 units on $X$-axis are

Which one of the following points lies inside a circle of radius 6 and centre at $(3,5)$ ?

For the equation $a x^2+b y^2+2 h x y+2 g x+2 f y+c=0$ where $a \neq 0$, to represent a circle, the condition will be

The equation of a circle whose end points of a diameter are $\left(\mathrm{x}_1, \mathrm{y}_1\right)$ and $\left(\mathrm{x}_2, \mathrm{y}_2\right)$ is

The circle $x^2 + y^2 - 2kx - 2ky + k^2 = 0$ touches the $x$-axis at $P$ and $y$-axis at $Q$. What is $PQ$ equal to?

What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are $x + y = 0$ and $x - y = 0$?

For $r \gt 0, f(r)$ is the ratio of perimeter to area of a circle of radius $r$. Then $f(1)+f(2)$ is equal to

Under which of the following conditions does a general second-degree equation $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0(a \neq 0)$ represent a circle?

What is the area enclosed by the equation $x^2+y^2=2$ ?

Let $\mathrm{C}$ be the centre and $\mathrm{A}$ be one end of a diameter of the circle $x^2+y^2-2 x-4 y-20=0$. If $P$ is a point on $A C$ such that $\mathrm{A}$ divides $\mathrm{CP}$ in the ratio $2: 3$, then the locus…

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

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 $\angle \mathrm{QPR}=$