If the locus of the point,whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$,is $ax^2+by^2+cxy+dx+ey+170=0$,then the value of $a^2+2b+3c+4d+e$ is equal to:

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 the angle between a pair of tangents drawn from a point $P$ to the circle $x^2+y^2-4x+2y+3=0$ is $\frac{\pi}{2}$,then 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

If the coordinates of a moving point $P$ are $(\cos \theta + \sin \theta, \sin \theta - \cos \theta)$,where $\theta$ is a parameter,find the locus of $P$.

From a point $P$ on the circle $x^2+y^2=4$,two tangents are drawn to the circle $x^2+y^2-6x-6y+14=0$. If $A$ and $B$ are the points of contact of those lines,then the locus of the centre of the circle passing through the points $P, A$ and $B$ is