If the ends of the hypotenuse of a right-angled triangle are $(0, a)$ and $(a, 0)$,then the locus of the third vertex is:

If $A = (a, 0)$ and $B = (-a, 0)$,then the locus of a point $P = (x, y)$ such that $PA^2 - PB^2 = a^2$ is.

At what time between $10\,\text{O'clock}$ and $11\,\text{O'clock}$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?

$A$ variable line passes through a fixed point $P$. If the algebraic sum of the perpendiculars drawn from $(2, 0)$,$(0, 2)$,and $(1, 1)$ to the line is zero,then the coordinates of the point $P$ are:

If $A(1,0), B(0,-2), C(2,-1)$ are three fixed points,then the equation of the locus of a point $P(x,y)$ such that the area of $\triangle PAB$ is equal to the area of $\triangle PAC$ is:

$A$ point $P$ moves on the line $2x - 3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points,then the locus of the centroid of $\Delta PQR$ is a line