### Home > CALC > Chapter 10 > Lesson 10.1.3 > Problem10-24

10-24.

Show that the curve whose parametric equations are $x(t) = t^3-3t$ and $y(t) = t^2$ intersects itself at $(0, 3)$. Find the equations for two tangent lines at the point of intersection.

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 $x\left(t\right)$ for these solutions?