If the coordinates of one end of a diameter of the circle $x^2+y^2+4x-8y+5=0$ are $(2,1)$, then the coordinates of the other end are:

Find the equation of the circle which touches the $X$-axis at a distance of $+3$ from the origin and cuts an intercept of $8$ on the positive $Y$-axis.

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} = $

The mid-point of the chord of the circle $x^2+y^2-6x+4y-12=0$ drawn parallel to the tangent at $(-1,1)$ and at a distance of one unit from the tangent is

Let $P$ and $Q$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$,respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is