What is the equation of the tangent to 3xy + y^2 - x^2 = 0 at the origin.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The equation of the tangent to the curve defined by 3xy + y^2 - x^2 = 0 at the origin (0, 0) has to be determined.

Use implicit differentiation to determine `dy/dx` . The value of `dy/dx` at (0,0) is the slope of the tangent at that point. Once the slope of the tangent is known the equation of the tangent can be determined.

The derivative y' is determined as 3xy' + 3y + 2y*y' - 2x = 0

=> y'(3x + 2y) = 2x - 3y

=> `dy/dx = (2x - 3y)/(3x + 2y)`

At (0, 0), the slope is `0/0` which is not defined.

The equation of the tangent to the curve 3xy + y^2 - x^2 = 0 at (0, 0) cannot be determined.

Approved by eNotes Editorial Team