Question

A particle moves along the curve y = x² + 2x. At what point(s) on the curve are the x and y coordinates of the particle changing at the same rate?

Answer 1

Given: a particle moves along the curve y = x² + 2x.

To find the points at which the curve are the x and y coordinates of the particle changing at the same rate

Equation of curve is y = x² + 2x

Differentiating the above equation with respect to x, we get

When x and y coordinates of the particle are changing at the same rate, we get

Now substitute the value from eqn(i), we get

Substitute this value of x in the given equation of curve, we get

Hence the points at which the curve are the x and y coordinates of the particle changing at the same rate is \((-\frac{1}{2},-\frac{3}{4})\)