What's the curve parallel to the parabola y=x^2y=x2?

1 Answer
Jun 15, 2017

The parametric equations are
(x,y) = (1/(2a)t- ((k)t)/sqrt(1-t^2), 1/(4a)t^2-k/sqrt(1-t^2))(x,y)=(12at(k)t1t2,14at2k1t2)

Where k is the distance from y = ax^2y=ax2

Explanation:

I found a good answer in a forum

I have written the parametric equations into the answer area.

Here is a graph of y = x^2y=x2 and its parallel curve with k = -1k=1:

Desmos.comDesmos.com

Here is a graph of y = x^2y=x2 and its parallel curve with k = 1k=1:

Desmos.comDesmos.com