The locus of the point which is equidistant from the point $(1,1)$ and the line $x+y+1=0$ is

The coordinates of the points $A$ and $B$ are $(ak, 0)$ and $(\frac{a}{k}, 0)$,where $k = \pm 1$. If a point $P(x, y)$ moves such that $PA = kPB$,then the equation to the locus of $P$ is:

The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant,is a circle whose centre is at the

The shortest distance between the curves $y^2 = x^3$ and $9x^2 + 9y^2 - 30y + 16 = 0$ is

The angle between the tangents drawn from a point $P$ to the circle $x^2 + y^2 + 4x - 2y - 4 = 0$ is $60^{\circ}$. The locus of $P$ is:

If $\frac{x}{\alpha} + \frac{y}{\beta} = 1$ touches the circle $x^2 + y^2 = a^2$,then the point $(\frac{1}{\alpha}, \frac{1}{\beta})$ lies on a/an