Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, -25) Directrix: y = 25

Solution:

Given directrix of y = 25 and focus (0, -25)

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

We are using distance formula √{(x - 0)² + (y - (-25))²} = |y - 25|

Applying square on both sides

⇒ (x)² + (y + 25)² = (y - 25)²

⇒ (y + 25)² - (y - 25)² = -(x)²

⇒ y² + 50y + 625 - (y² - 50y + 625) = -x²

⇒ y² + 50y + 625 - y² + 50y - 625 = -x²

⇒ 100y = -x²

⇒ y = x² /100

The quadratic equation created is y = x²/100.

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, -25) Directrix: y = 25

Summary:

The standard form of the equation of each parabola satisfying the given conditions. Focus: (0, -25) Directrix: y = 25 is y = x²/100.