$A(-4,0)$ and $B(4,0)$ are two fixed points. $C$ and $D$ are two points on the $Y$-axis such that $CD=4$ and $C$ is a point below $D$. Then the locus of the point of intersection of the lines $AC$ and $BD$ is

$p, x_1, x_2, \ldots, x_n$ and $q, y_1, y_2, \ldots, y_n$ are two arithmetic progressions with common differences $a$ and $b$ respectively. If $\alpha$ and $\beta$ are the arithmetic means of $x_1, x_2, \ldots, x_n$ and $y_1, y_2, \ldots, y_n$ respectively,then the locus of $P(\alpha, \beta)$ is

Let $A = (a, 0)$ and $B = (-a, 0)$ be two fixed points. For $a \in (-\infty, 0)$,point $P(x, y)$ moves in the plane such that $PA = nPB$ $(n \neq 0, 1)$. If $n = 1$,find the locus of point $P$.

If the distance of any point $P(x, y)$ from the points $A(a + b, a - b)$ and $B(a - b, a + b)$ are equal,then the locus of $P$ is:

Let $BC$ be a fixed line segment in the plane. The locus of a point $A$ such that the $\triangle ABC$ is isosceles,is (with finitely many possible exceptional points)

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is