### Home > CALC > Chapter Ch10 > Lesson 10.1.3 > Problem 10-24

10-24.

Show that the curve whose parametric equations are *x*(*t*) = *t*^{3} −3*t *and *y*(*t*) = *t*^{2} intersects itself at (0, 3). Find the equations for two tangent lines at the point of intersection. Homework Help ✎

Notice that *y*(*t*) = *t*^{2}. At the point (0, 3), *t*^{2} = 3. How many solutions does this equation have?

What is the value of *x*(*t*) for these solutions?

To compute the slopes of the tangent lines at this point, use: