Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1

D

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

= | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = (x + 5)² ← add 2 to both sides

y = (x + 5)² + 2

or

f(x) = (x + 5)² + 2 → D

answer is x<

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.