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

If $A (c, 0)$ and $B (-c, 0)$ are two points,find the locus of point $P$ such that $PA^{2} + PB^{2} = AB^{2}$.

If the sum of the distances of a point from the origin and the line $x = 2$ is $4$,then its locus is

For all values of $\theta$,the locus of the point of intersection of the lines $x \cos \theta + y \sin \theta = a$ and $x \sin \theta - y \cos \theta = b$ is

Let $\Gamma$ be a circle with diameter $AB$ and centre $O$. Let $l$ be the tangent to $\Gamma$ at $B$. For each point $M$ on $\Gamma$ different from $A$,consider the tangent $t$ at $M$ and let it intersect $l$ at $P$. Draw a line parallel to $AB$ through $P$ intersecting $OM$ at $Q$. The locus of $Q$ as $M$ varies over $\Gamma$ is

If $A=(1,2)$,$B=(2,1)$ and $P$ is any point satisfying the condition $PA+PB=3$,then the equation of the locus of $P$ is