Equation of common tangent to parabola $y^2=40x$ and circle $x^2+y^2=50$ may be

If parabola $y^2=4ax$ touches circle $x^2+y^2+2gx=0$ externally, then

From point $A(-2, 0),$ tangents $AB$ and $AC$ are drawn to the parabola $y^2=8x.$ A circle is drawn passing through the focus of the parabola and touching it at $B$ and another circle is drawn passing through the focus of the parabola and touching it at $C.$ Which of the following points with respect to $∆ABC$ lie on the common chord of the two circles?

From the vertex of the parabola $y^2=4ax,$ a pair of mutually perpendicular chords are drawn and with these chords as adjacent sides, a rectangle is completed. The locus of the farther angle of the rectangle is

Extremities of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a>b\right)$ having a major axis $2a$ lies on:

Let $A, B, C$ be co-normal points on the parabola $y^2=4ax.$ Which of the following statements are true?

Which of the following equations in parametric form represent a hyperbola?