Parametric Curves: Tangent Lines

[chefstef00]

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]

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]

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]

Duh, right. Make that 'one' cubic.

 

[chefstef00]

thanks a lot for the help, i was able to find the second equation, thanks

 

[davros72]

So what *is* that second equation? I'm stuck!