If the straight line $y=mx$ lies outside of the circle $x^2+y^2-20y+90=0$,then the value of $m$ will satisfy

If the lines $12x - 5y - 17 = 0$ and $24x - 10y + 44 = 0$ are tangents to the same circle,then the radius of the circle is:

If $Q(h, k)$ is the inverse point of the point $P(1, 2)$ with respect to the circle $x^2+y^2-4x+1=0$,then $2h+k=$

Let the slope of a diameter $AC$ of a circle of radius $25$ units be $\frac{3}{4}$. If $(3, 2)$ is the centre of the circle,$A = (x_1, y_1)$ and $C = (x_2, y_2)$,then $\frac{x_1 x_2}{y_1 y_2} = $

Find the number of common tangents that can be drawn to the circles $x^2 + y^2 - 4x - 6y - 3 = 0$ and $x^2 + y^2 + 2x + 2y + 1 = 0$.

If the two circles $(x-1)^2+(y-3)^2=r^2$ and $x^2+y^2-8x+2y+8=0$ intersect at two distinct points,then