$A$ point moves such that its distance from the point $(-1, 0)$ is always three times its distance from the point $(0, 2)$. The locus of the point is

The set of all real values of $\lambda$ for which the point $P$ with coordinates $(\lambda, \lambda^2)$ does not lie inside the triangle formed by the lines $x - y = 0$, $x + y - 2 = 0$, and $x + 3 = 0$ is:

The locus of the centre of a circle which passes through the origin and cuts off a length of $4$ units from the line $x=3$ is

If a circle of constant radius $3k$ passes through the origin $O$ and meets the coordinate axes at $A$ and $B$,then the locus of the centroid of the triangle $OAB$ is

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

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