Question

Find the equation of a parabola with focus F(-3, 9) and directrix x = -13.

Answer 1

Answer:

y² = 38x + 79

Step-by-step explanation:

Since directrix is the line x = -13, then it means x + 13 = 0

Focus is F(-3, 9).

Let A(x, y) be any point inside the plane having the focus and directrix.

Let MA be the perpendicular distance from A to the directrix and it means that A lies on parabola provided FA = MA.

Thus;

√[(x - (-3))² + (y - 9)²] = (x + 13)

Squaring both sides gives;

(x + 3)² + (y - 9)² = (x + 13)²

>> (x² + 6x + 9) + (y² - 18x + 81) = x² + 26x + 169

>> 6x + 9 + y² - 18x + 81 = 26x + 169

>> y² = 26x + 12x + 169 - 90

>> y² = 38x + 79