Mathematics
tattie
13

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

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(1) Answers
jeanette54

check the picture below [latex]\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[/latex]

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