Derive the Equation of the Parabola with a Focus at (-5, 5) and a Directrix of y = -1.
We will be solving this by using the focus point and the directrix.
Answer: The Equation of the Parabola with a Focus at (-5, 5) and a Directrix of y = -1 is x2 + 10x - 12y + 49 = 0.
Let us solve this step by step.
Explanation:
Given that, Focus = (-5, 5) and directrix y = -1
Let us suppose that there is a point (x, y) on the parabola.
Its distance from the focus point (-5, 5) is √(x + 5)2 + (y - 5)2
Its distance from directrix y = -1 is |y + 1|
Therefore, the equation will be:
√(x + 5)2 + (y - 5)2 = |y + 1|
Apply square on both sides.
(x + 5)2 + (y - 5)2 = (y + 1)2
x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1
x2 + 10x - 12y + 49 = 0