Let a variable line passing through the centre of the circle $x^2+y^2-16x-4y=0$ meet the positive coordinate axes at points $A$ and $B$. Then the minimum value of $OA+OB$,where $O$ is the origin,is equal to

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of the perpendicular from $O$ on $AB$ is

$A$ point $P(x, y)$ moves such that the sum of the squares of its distances from the points $(1, 2)$ and $(-2, 1)$ is $14$. Let $f(x, y) = 0$ be the locus of $P$,which intersects the $x$-axis at points $A, B$ and the $y$-axis at points $C, D$. Then the area of the quadrilateral $ACBD$ is equal to:

Given two fixed points $A(-2, 1)$ and $B(3, 0)$,find the locus of a point $P$ which moves such that the angle $\angle APB$ is always a right angle.

If $t \in R - \{-1\}$,then the locus of the point $\left(\frac{3at}{1+t^3}, \frac{3at^2}{1+t^3}\right)$ is

The locus of the points from which perpendicular tangents can be drawn to the circle $x^2 + y^2 = a^2$ is