The equation of parabola is expressed as: y² = -20x
What is the equation of the parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.
The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given, vertex = (0, 0)
Focus = (-5, 0)
We have to find the equation of the parabola.
The equation is of the form y = -ax²
Directrix x = 5.
As every point on parabola is equidistant from focus and directrix, the equation will be
y² + (x + 5)² = (x - 5)²
y² + x² + 10x + 25 = x² - 10x + 25
y² = - 10x - 10x
y² = -20x
Therefore, the equation of parabola is y² = -20x