The locus of points $(x, y)$ in the plane satisfying $\sin ^2 x + \sin ^2 y = 1$ consists of

If $P(x, y)$ is a variable point which is at a distance of $2$ units from the line $2x - 3y + 1 = 0$ and $\sqrt{13}$ units from the point $(5, 6)$,then the equation of the locus of $P$ is:

Let $a \neq 0, b \neq 0, c$ be three real numbers and $L(p, q) = \frac{ap + bq + c}{\sqrt{a^2 + b^2}}, \forall p, q \in \mathbb{R}$. If $L\left(\frac{2}{3}, \frac{1}{3}\right) + L\left(\frac{1}{3}, \frac{2}{3}\right) + L(2, 2) = 0$,then the line $ax + by + c = 0$ always passes through the fixed point:

$A(a, 0)$ and $B(-a, 0)$ are two fixed points. If $\angle A - \angle B = \theta$,what is the locus of point $C$ of triangle $ABC$?

Let $A, B$ and $C$ be three points in a plane. The locus of a point $P$ moving such that $PA^2 + PB^2 = 2PC^2$ is a

If $2a + b + 3c = 0$,then the line $ax + by + c = 0$ passes through the fixed point that is