Problem 20

Given information

The equation of ellipse 

Where 

To find: The equation of the set of all points from the curve of slops are negative reciprocal. 

Step-by-step explanation

Since the geneneral equation for A tangent line is:

let us consider same for tangent  to the ellipse

 the discriminant of the equation, is zero  as ellipse intersect the tangent at one point only

The standard form of ellipse equation 

A tangent line to the ellipse

The line intersect exactly one point on the ellipse

Substitute  in equation (1)