Hello, macho_maggot2001!

Welcome aboard!

A curve is defined parametrically by the equations: .

Find:

1) the equations of the normals to the curve at the points

. . .where the curve meets the x-axis.

2) the coordinates of their point of intersection.

1) The curve meets the x-axis when

. .

Then: .

. . The x-intercepts are: .

Then we need the derivative, , to find the slope of the tangents.

We have: .

When

When

One normal has point and

. . Its equation is: .

The other has point and

. . Its equation is: .

2) They intersect when: .

. . .

Their intersection is: .