Question

Write the vertex form of the parabola with the focus (-68/8,-7) and Directrix x=-65/8

Answer 1

A parabola is the locus of all points equidistant from a point called focus and a line called directrix.

Answer 2

Applying the above gives
\[\left(x+\frac{68}{8}\right)^2+(y
+7)^2=\left(x+\frac{65}{8}\right)^2

\]

Answer 3

\[
(y+7)^2=\left(x+\frac{65}{8}\right)^2-\left(x+\frac{68}{8}\right)^2 \\
(y+70)^2=-\frac{1}{4}
\left(x+\frac{133}{16}\right
)
\]

Answer 4

See the graph.