Locus of the points from which perpendicular tangent can be drawn to the circle ${x^2} + {y^2} = {a^2}$, is
A circle passing through origin
A circle of radius $2a$
A concentric circle of radius $a\sqrt 2 $
None of these
The circles ${x^2} + {y^2} - 10x + 16 = 0$ and ${x^2} + {y^2} = {r^2}$ intersect each other in two distinct points, if
The line $L$ passes through the points of intersection of the circles ${x^2} + {y^2} = 25$ and ${x^2} + {y^2} - 8x + 7 = 0$. The length of perpendicular from centre of second circle onto the line $L$, is
The points of intersection of the circles ${x^2} + {y^2} = 25$and ${x^2} + {y^2} - 8x + 7 = 0$ are
The equation of director circle of the circle ${x^2} + {y^2} = {a^2},$ is
$P$ is a point $(a, b)$ in the first quadrant. If the two circles which pass through $P$ and touch both the co-ordinate axes cut at right angles, then :