# Parametric Curves: Tangent Lines

## Homework Statement

Find equations of the tangents to the curve x=3t^2+1, y=2t^3+1 that pass through the point (4,3).

## The Attempt at a Solution

I was able to find the equation y=x-1 as a tangent line through the point (4,3) for the part of the curve above the x-axis since (4,3) is on the curve.

However, I do not know how to find the equation of the tangent for the part of the curve below the x-axis since I do not know what point on the curve the tangent passes through and therefore do not know the t value.

Any help is appreciated, thanks

Dick
Homework Helper
Write down the equation for the tangent line to the curve at general value of t. Now put in the condition (4,3) is on the line. You should get a couple of cubic equations. You already know t=1 is a solution. Is there another?

HallsofIvy
Homework Helper
Well, you get a cubic equation. Knowing that t= 1 is a solution makes it easy to solve. Dick's suggestion is right on the money.

Dick