# Math Help - Tangents to Parametric Curves

1. ## Tangents to Parametric Curves

The parametric curve:

x(t) = 9cos(t)
y(t) = 3sin(2t)

intersects itself at which point? What are the two slopes to the tangent at this point?

2. Did you graph it?. You have a leminscate. It looks like the 'infinity' symbol.

The slope is given by $\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{dy}{dx}$

$y'(t)=6cos(2t)$

$x'(t)=-9sin(t)$

$\frac{6cos(2t)}{-9sin(t)}$

To find the slope at its intersection point, plug in $t=\frac{\pi}{2}$