Find and equation of the parabola described 1. Focus (2,0): directrix r 2

1)

Parabola:

A parabola is an arc shaped curve in which every point on the curve is at an equal distance from a fixed point called Focus and a fixed straight line called Directrix.

The focus and Directrix of the parabola are (2, 0) and x = –2 respectively.

It is known that the distance between any point and the focus of the parabola is same as that of the distance between that point and the directrix of the parabola.

Let (x₀, y₀) be a point on the parabola.

The distance between the point (x₀, y₀) and the focus (2, 0) is, $\sqrt{{\left(x_0-2\right)}^2+{\left(y_0-0\right)}^2}$.

The distance between (x₀, y₀) and the directrix x = –2 is $\left|x_0-\left(-2\right)\right|=\left|x_0+2\right|$.