Problem 66

Given information

We are given the equation 

The given equation has a tangent line when with equation 

And a tangent line when with equation 

Step-by-step explanation

There are two things to note :

y-coordinates of the tangent and that of the curve are equal at the point where they touch.

The slope of the tangent and that of the curve are equal at the point where they touch.

 

Given that  is a tangent at

y-coordinate when   is  

Therefore the point   point lies on the given curve .

Substitute   and   in the main equation  . To get