The locus of the point of intersection of perpendicular tangents to the circle $x^{2}+y^{2}=16$ is

The equation $r \cos \theta = 2 a \sin^2 \theta$ represents the curve

The locus of a point $(x, y)$ whose distance from the point $(-g, -f)$ is always $a$,where $k = g^2 + f^2 - a^2$,is:

The circle passing through the distinct points $(1, t)$,$(t, 1)$,and $(t, t)$ for all values of $t$ passes through the point:

The locus of the vertex $A$ of a triangle $ABC$,where the base $BC$ is fixed and the perimeter of the triangle is constant,is

The angle between a pair of tangents drawn from a point $P$ to the circle $x^{2}+y^{2}+4x-6y+9 \sin^{2} \alpha + 13 \cos^{2} \alpha = 0$ is $2 \alpha$. The equation of the locus of the point $P$ is