From a point $A(1, 0)$ on the circle $x^2+y^2-2x+2y+1=0$,a chord $AB$ is drawn and it is extended to a point $P$ such that $AP=3AB$. The equation of the locus of $P$ is

If the coordinates of a point are given by the equations $x = a(1 - \cos \theta )$ and $y = a\sin \theta $,then the locus of the point will be

The centres of a set of circles,each of radius $3$,lie on the circle ${x^2} + {y^2} = 25$. The locus of any point in the set is

The equation of the image of the circle $x^2 + y^2 + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is:

The locus of the centres of the circles,which cut the circles $x^2+y^2+4x-6y+9=0$ and $x^2+y^2-5x+4y+2=0$ orthogonally,is

Let the circle $x^{2}+y^{2}=4$ intersect the $x$-axis at the points $A(a,0), a>0$ and $B(b,0)$. Let $P(2 \cos \alpha, 2 \sin \alpha), 0 < \alpha < \frac{\pi}{2}$ and $Q(2 \cos \beta, 2 \sin \beta)$ be two points such that $(\alpha - \beta) = \frac{\pi}{2}$. Then the point of intersection of $AQ$ and $BP$ lies on: