I thought I solved this correctly, but my answer was marked wrong:

Here it is: Find the equations of the tangents to this curve that pass through the point (15,15).

Solution:

Substituting in the point (15,15):

After simplifying, this turns into:

Setting t=1:

is my first tangent line, which was wrong. When I graphed it, it did appear to be tangent to the curve at that point..

Setting t=-2:

also incorrect.

If someone could fix my work, I'd be very very thankful.