If $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ is the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p$,where $0 < p < a$,then $\lambda=$

$A$ circle $S \equiv x^2+y^2-16=0$ intersects another circle $S^{\prime}=0$ of radius $5$ units such that their common chord is of maximum length. If the slope of that chord is $\frac{3}{4}$,then the centre of such a circle $S^{\prime}=0$ is

The radical centre of the three circles $x^2+y^2-1=0$,$x^2+y^2-8x+15=0$ and $x^2+y^2+10y+24=0$ is

Find the equation of a circle with radius $3$ that touches the circle $x^{2} + y^{2} - 4x - 6y - 12 = 0$ internally at the point $(-1, -1)$.

The distance between the centres of similitude of the circles $x^2+y^2+6x-8y+16=0$ and $x^2+y^2-2x-2y+1=0$ is

If the centre of a circle,which passes through the points of intersection of the circles $x^2 + y^2 - 6x + 2y + 4 = 0$ and $x^2 + y^2 + 2x - 4y - 6 = 0$,lies on the line $y = x$,then the equation of the circle is: