# The equations #{(y = c x^2+d, (c > 0, d < 0)),(x = a y^2+ b, (a > 0, b < 0)):}# have four intersection points. Prove that those four points are contained in one same circle ?

##### 1 Answer

Sep 14, 2016

See below.

#### Explanation:

Making the following transformations

and comparing with the generic circle equation

we conclude that with

As an example, using the values

we obtained the following outcome.