A curve is described by the parametric equations x = t^2 + 2t and y = t^3 + t^2. An equation of the line tangent to the curve at the point determined by t = 1 is...?

Answer 1

x = t² + 2t and y = t³ + t²

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) = (3t² + 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)