What is an equation of the parabola with vertex at the origin and focus (-5, 0)

Solution:

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

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What is an equation of the parabola with vertex at the origin and focus (-5, 0)

Summary:

The equation of a parabola with vertex (0, 0) and focus (-5, 0) is y² = -20x.