### Home > APCALC > Chapter 10 > Lesson 10.1.3 > Problem10-34

10-34.

Show that the curve whose parametric equations are $x(t) = t^ 3 - 3t$ and $y(t) = t ^2$ intersects itself at $(0, 3)$. Write the equations of the 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 $x(t)$ for these solutions?

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

$\frac{dy/dt}{dx/dt}$