Find the equation of the parabola that satisfies the following conditions: Focus $(6, 0)$,directrix $x = -6$.

The locus of the vertices of the family of parabolas $y = \frac{a^3 x^2}{3} + \frac{a^2 x}{2} - 2a$ is

Find the equation of the normal to the curve $x^{2}=4y$ which passes through the point $(1,2)$.

$A$ ray of light moving parallel to the $x$-axis gets reflected from a parabolic mirror whose equation is $(y - 2)^2 = 4(x + 1)$. After reflection,the ray must pass through the point:

Tangents at the extremities of any focal chord of a parabola intersect

If $x-2y+k=0$ is a tangent to the parabola $y^2-4x-4y+8=0$,then the slope of the tangent drawn at $(1, k)$ on the given parabola is