A point moves a long the curve of
Careful! Notice that the derivative is given as change in
What is shown was a part of an implicit differentiation problem.
This is a related rates problem.
The question is asking about the rate that the secant line between the moving point and the vertex is
changing at the moment when that moving point is at
Start by finding the equation of a secant line that connects an arbitrary point
You could use the Pythagorean Theorem--note, you do not have to solve for
Implicitly differentiate that equation with respect to time.
Also, evaluate the change
You will find the rate that the distance will change when the moving point reaches