Answer to Question #248647 in Analytic Geometry for Carol

Question

Vertex (7,11), directrix x-1 standard equation of parabola

Answer 1

The equation of the parabola has the form $(y-b)^2=2p(x-a)$ , where $(a;b)$ is a vertex of parabola, so $a=7, b=11$. $x=-\frac{p}{2}$ is a directrix . Vertex is halfway between focus and direcrix. The focus lies to the right side of the directrix, so the parabola opens to the right. As $x=1$ , so $p=7-1=6$. The focus of the parabola has coordinates $(12;0)$. So the standard equation of parabola is $(y-11)^2=12(x-7)$