Find the equation of the parabola with vertex at (0,0)and focus at (0,5).
A) $x ^ { 2 } = 20 y$
B) $x ^ { 2 } = 5 y$
C) $y ^ { 2 } = 20 x$
D) $x ^ { 2 } = y + 5$
E)none of these

Question

Find the equation of the parabola with vertex at (0,0)and focus at (0,5). ​
A) $x ^ { 2 } = 20 y$
B) $x ^ { 2 } = 5 y$
C) $y ^ { 2 } = 20 x$
D) $x ^ { 2 } = y + 5$
E)none of these

Quizplus · Accepted Answer

The equation of a parabola with its vertex at the origin (0,0) and focus at (0,5) is of the form $x^2 = 4py$, where $p$ is the distance from the vertex to the focus, which is 5 in this case. Plugging $p = 5$ into the equation gives $x^2 = 20y$.

Find the Equation of the Parabola with Vertex at (0,0)and x2=20yx ^ { 2 } = 20 yx2=20y

Find the Equation of the Parabola with Vertex at (0,0)and $x ^ { 2 } = 20 y$