The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

The parabolas $ax^2 + 2bx + cy = 0$ and $dx^2 + 2ex + fy = 0$ intersect on the line $y = 1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in $G.P.$,then

The equations of the tangents to the parabola $y^2 = 4ax$ at the ends of its latus rectum are-

The equation of the tangent at $(-4, -4)$ on the curve $x^2 = -4y$ is

The vertex of a parabola is $(2, 2)$ and the coordinates of the two extremities of its latus rectum are $(-2, 0)$ and $(6, 0)$. The equation of the parabola is

If the normal drawn at the point $P(9, 9)$ on the parabola $y^2 = 9x$ meets the parabola again at $Q(a, b)$,then $2a + b =$