What is the equation of the tangent to the curve $x^2 + y^2 = a^2$ at the point $\left( \frac{a}{\sqrt{2}}, \frac{a}{\sqrt{2}} \right)$?

The equations of the tangent to the circle $5x^2 + 5y^2 = 1$ parallel to the line $3x + 4y = 1$ are

Let the tangent to the circle $x^{2}+y^{2}=25$ at the point $R(3,4)$ meet the $x$-axis and $y$-axis at points $P$ and $Q$,respectively. If $r$ is the radius of the circle passing through the origin $O$ and having its centre at the incentre of the triangle $OPQ$,then $r^{2}$ is equal to

When will the line $y = x + c$ intersect the circle $x^2 + y^2 = 1$ at two coincident points?

Find the equations of the tangents drawn to the circle $x^2+y^2=50$ at the points where the line $x+7=0$ meets it.

The area of the triangle formed by the positive $X$-axis,the tangent and the normal to the curve $x^2+y^2=16a^2$ at the point $(2\sqrt{2}a, 2\sqrt{2}a)$ is