The point on the curve ${y^2} = 2(x - 3)$ at which the normal is parallel to the line $y - 2x + 1 = 0$ is

The equations of tangents to the circle $x^2 + y^2 - 22x - 4y + 25 = 0$ which are perpendicular to the line $5x + 12y + 8 = 0$ are

Statement $(A) :$ For all values of $\theta$,the line $(x - 3) \cos \theta + (y - 3) \sin \theta = 1$ is tangent to the circle $(x - 3)^2 + (y - 3)^2 = 1$.
Reason $(R) :$ For all values of $\theta$,the line $x \cos \theta + y \sin \theta = a$ is tangent to the circle $x^2 + y^2 = a^2$.

The equation of the tangent to the curve $x^2+y-7=4x$ at the point $(1,10)$ is

The angle between the tangents drawn from the point $P(k, 6k)$ to the circle $x^2+y^2+6x-6y+2=0$ is $2 \operatorname{Tan}^{-1}\left(\frac{4}{3}\right)$. If the coordinates of $P$ are integers,then $k=$

Let a circle $C$ of radius $5$ lie below the $x$-axis. The line $L_{1}: 4x + 3y + 2 = 0$ passes through the centre $P$ of the circle $C$ and intersects the line $L_{2}: 3x - 4y - 11 = 0$ at $Q$. The line $L_{2}$ touches $C$ at the point $Q$. Then the distance of $P$ from the line $5x - 12y + 51 = 0$ is