### Home > PC3 > Chapter 10 > Lesson 10.1.4 > Problem10-77

10-77.

On graph paper, sketch the parabola that is the set of all points equidistant from the focus $(0, 7)$ and the directrix $y = −3$.

1. Use the definition to write and simplify the equation of the parabola.

The distance from any point on the parabola, $(x, y)$, to the focus is $\sqrt{(x − 0)^2 + (y − 7)^2}$ .
The distance from any point on the parabola, $(x, y)$, to the directrix is √ $\sqrt{(x − x)^2 + (y − (−3))^2}$ .

2. Change the equation of this parabola to shift the graph $5$ units to the right.