If the pair of tangents drawn to the circle $x^2+y^2=a^2$ from the point $(10,4)$ are perpendicular,then $a=$

The circle $x=5 \cos \theta, y=5 \sin \theta$ is bounded by the rectangle formed by the lines $x \pm 6=0$ and $y \pm 6=0$. The area of the triangle that lies inside the rectangle,which is formed by the tangent at $P\left(\frac{2 \pi}{3}\right)$ to the circle with two of the above given lines,is

Find the points on the curve $x^{2}+y^{2}-2x-3=0$ at which the tangents are parallel to the $x$-axis.

The equation of the tangent to the circle $x^2 + y^2 = a^2$ which is parallel to the line $y = mx + c$ is:

The slope of the common tangent drawn to the circles $x^2+y^2-4x+12y-216=0$ and $x^2+y^2+6x-12y+36=0$ is

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+C=0$,then $C=$