implicit derivatives

The curve (C) is described by the following equation;
(x^2+y^2)^2=k^2*(x^2-y^2), k>0;
a) Find the slope of the tangent of (C) at point P (x0, y0), y0≠ 0;

b) Identify the points of (C) where the tangent is parallel to x-axis.

How to make it in Matlab?I have no idea

Answer 1

[Walter Roberson]

The slope of the tangent of C at a point is the same as the derivative at that point.

If you solve for y in terms of x and k, then you can take derivatives.

However, you will find that there are 4 solutions, and you will probably run in to imaginary numbers in at least 2 of them (that is, two of the four might give solutions that are always imaginary for a given k.). The two that have real-valued solutions need to be considered carefully. You may have to give a solution that is conditional on the value of one or more variable.

Hint: if you use symbolic expressions, diff() and solve() are relevant.