Write Equations of Parabolas in Standard Form
-Focus: $( 2,5 )$; Directrix: $y = - 3$
A) $( x - 2 ) ^ { 2 } = 16 ( y - 1 )$
B) $( y - 2 ) ^ { 2 } = 16 ( x - 1 )$
C) $( x - 1 ) ^ { 2 } = 16 ( y - 2 )$
D) $( y - 1 ) ^ { 2 } = 16 ( x - 2 )$

Question

Quizplus · Accepted Answer

The focus of the parabola is (2,5), and the directrix is $y = -3$. The vertex is midway between the focus and the directrix, so it is at $y = 1$ (since $5 - (-3) = 8$ and half of 8 is 4, moving 4 units down from the focus gives $5 - 4 = 1$). The vertex is also at $x = 2$, the same x-coordinate as the focus. The distance from the vertex to the focus or directrix is 4, so the parabola opens upwards, and the equation is in the form $(x - h)^2 = 4p(y - k)$, where $h = 2$, $k = 1$, and $p = 4$, making the equation $(x - 2)^2 = 16(y - 1)$.

Write Equations of Parabolas in Standard Form -Focus (2,5)( 2,5 )(2,5)

Write Equations of Parabolas in Standard Form
-Focus $( 2,5 )$