Question

Write the equation of a parabola with its vertex at the origin and directrix at y = 1

a. X^2=y
b.Y^2=X
c.X^2=-4y
d.Y^2=-4x

Answer 1

check the picture below


`\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h = 0\\ k = 0\\ p=-1 \end{cases}\implies (x-0)^2=4(-1)(y-0)\implies x^2=-4y \\\\\\ -\cfrac{1}{4}x^2=y`