Find the standard form of the parabola with the given characteristics.focus: (2, 9) vertex: (2, 4) A)(x - 2)² = 20(y - 4) B)(x + 2)² = 20(y + 4) C)(x - 4)² = 20(y - 2) D)(x + 4)² = 20(y + 2) E)(x + 2)² = 5(y + 4)

Question

Quizplus · Accepted Answer

The standard form of a parabola is given by $(x - h)^2 = 4p(y - k)$ for a parabola that opens upwards or downwards, where $(h, k)$ is the vertex of the parabola and $p$ is the distance from the vertex to the focus. Given the vertex $(2, 4)$ and the focus $(2, 9)$, we can see that the parabola opens upwards and the distance $p$ from the vertex to the focus is $9 - 4 = 5$. Therefore, substituting $h = 2$, $k = 4$, and $p = 5$ into the standard form equation, we get $(x - 2)^2 = 20(y - 4)$, which matches choice A.

Find the Standard Form of the Parabola with the Given