If one end of a diameter of the circle $x^2 + y^2 - 3x + 8y - 4 = 0$ is $(6, -3)$,then what is the other end of the diameter?

The triangle $PQR$ is inscribed in the circle $x^2 + y^2 = 25$. If $Q$ and $R$ have coordinates $(3, 4)$ and $(-4, 3)$ respectively,then $\angle QPR$ is equal to

Let the centre of the circle be in the first quadrant and lie on the line $2x - y = 4$. Let the area of an equilateral triangle inscribed in the circle be $27\sqrt{3}$. Then the square of the length of the chord of the circle on the line $x = 1$ is . . . . . .

Find a possible equation of a chord of the circle $x^2 + y^2 = 100$ which passes through the point $(1, 7)$ and makes an angle of $\frac{2\pi}{3}$ with the origin.

Let $y=x$ be the equation of a chord of the circle $C_{1}$ (in the closed half-plane $x \ge 0$) of diameter $10$ passing through the origin. Let $C_{2}$ be another circle described on the given chord as its diameter. If the equation of the chord of the circle $C_{2}$, which passes through the point $(2, 3)$ and is farthest from the center of $C_{2}$, is $x+ay+b=0$, then $a-b$ is equal to:

If $A(-1,3)$ and $B(5,3)$ are points on a circle $C$ and the chord $AB$ subtends an angle $\pi / 4$ at a point $P$ on $C$,then the equation of such a circle $C$ is