Write Equations of Parabolas in Standard Form
-Focus: $( 13,0 )$; Directrix: $x = - 13$
A) $y ^ { 2 } = 52 x$
B) $y ^ { 2 } = - 52 x$
C) $y ^ { 2 } = 13 x$
D) $x ^ { 2 } = 52 y$

Question

Quizplus · Accepted Answer

The focus of the parabola is at (13,0), and the directrix is the vertical line x = -13. This means the parabola opens to the right. The distance from the focus to the vertex is 13 units, and the vertex is at the midpoint between the focus and the directrix, which is at the origin (0,0). The standard form of a parabola opening to the right is $y^2 = 4px$, where $p$ is the distance from the vertex to the focus, so $p = 13$. Therefore, the equation is $y^2 = 4(13)x = 52x$.

Write Equations of Parabolas in Standard Form -Focus (13,0)( 13,0 )(13,0)

Write Equations of Parabolas in Standard Form
-Focus $( 13,0 )$