Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Focus: $( 2,8 ) ;$ Directrix: $y = 0$
A) $( x - 2 ) ^ { 2 } = 16 ( y - 4 )$
B) $( y - 2 ) ^ { 2 } = 16 ( x - 4 )$
C) $( x - 4 ) ^ { 2 } = 16 ( y - 2 )$
D) $( y - 4 ) ^ { 2 } = 16 ( x - 2 )$

Question

Quizplus · Accepted Answer

The standard form of a parabola with a vertical axis is $(x - h)^2 = 4p(y - k)$, where $(h, k)$ is the vertex and $p$ is the distance from the vertex to the focus or directrix. Given the focus $(2, 8)$ and directrix $y = 0$, the vertex is halfway between the focus and directrix, at $(2, 4)$. The distance $p$ is 4, making the equation $(x - 2)^2 = 16(y - 4)$.

Write Equations of Parabolas in Standard Form Find the Standard (2,8);( 2,8 ) ;(2,8);

Write Equations of Parabolas in Standard Form
Find the Standard $( 2,8 ) ;$