Mark M. answered • 04/08/21

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

x = t^{2} + 2t and y = t^{3} + t^{2}

When t = 1, x = 3 and y = 2. So, (3,2) is the point of tangency

Slope of tangent = dy/dx evaluated when t = 1.

dy/dx = (dy/dt) / (dx/dt) = (3t^{2} + 2t) / (2t + 2) = 5/4 (when t = 1)

Equation of tangent line: y - 2 = (5/4)(x - 3)

Simplify to get y = (5/4)x - (7/4)

Aaron J.

That is much easier than expected. Thank you for the help!04/08/21