QuestionWhat is the focus of the parabola in the standard form equation $(x+3)^{2}=20(y-6) ?$ (A) $(6,2)$ (B) $(-3,11)$ (C) $(2,6)$ (D) $(11,-3)$

Studdy Solution
Determine the coordinates of the focus using the vertex $(h, k)$ and the value of $p$.
Since the parabola opens upwards (as indicated by the $(x-h)^2$ form), the focus will be $p$ units above the vertex. Therefore, the coordinates of the focus are: $$(h, k + p) = (-3, 6 + 5) = (-3, 11)$$
The focus of the parabola is $(-3, 11)$, which corresponds to option (B).