If $\theta$ is the angle made by the common tangent to the circle $x^2+y^2=16$ and the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ with the positive $X$-axis,then $\cos 2 \theta=$

$A$ common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8x$ is

Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$.
Statement-$1$: These tangents are perpendicular to each other.
Statement-$2$: From every point on the circle $x^2 + y^2 = 338$,perpendicular tangents can be drawn to the given circle.

The angle of intersection between the curves $y^2+x^2=a^2 \sqrt{2}$ and $x^2-y^2=a^2$ is

Let the point $P$ be the vertex of the parabola $y = x^2 - 6x + 12$. If a line passing through the point $P$ intersects the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ at the points $R$ and $S$, then the maximum value of $(PR + PS)^2$ is:

The equation of the circle symmetric to the circle $x^2 + y^2 - 2x - 4y + 4 = 0$ about the line $x - y = 3$ is