If $ABC$ is an isosceles triangle and the coordinates of the base points are $B(1, 3)$ and $C(-2, 7)$, then the coordinates of $A$ can be:

Let $A(5, -3)$,$B(3, -2)$,and $C(-1, 5)$ be three points. If $P$ is a point satisfying the condition $PA^2 + 2PB^2 = 3PC^2$,then a point that lies on the locus of $P$ is

Ten ants are on the real line. At time $t=0$,the $k$-th ant starts at the point $k^2$ and,travelling at a uniform speed,reaches the point $(11-k)^2$ at time $t=1$. The number of distinct times at which at least two ants are at the same location is

If the point $(x, y)$ is equidistant from the points $(a + b, b - a)$ and $(a - b, a + b)$,then:

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

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