Thread: Eliminate the param

I tried searching but most what I found was related to Trig. Not sure if this is even calculus, but it's in my calc class, so here goes...

Eliminate the parameter t to find a Cartesian equation for:

x = t²
y = 5 + 3t
x = Ay² + By + C

where A = ??, B = ?? and C = ??

This is supposedly review, but I sure don't know what I'm doing here. Thanks in advance!

Hey jjtjp.

Hint: Try squaring y as a function of t and sub in x whenever there is a t^2 (or sub in SQRT(x) = |t| for these terms) and collect and simplify.

Originally Posted by jjtjp

I tried searching but most what I found was related to Trig. Not sure if this is even calculus, but it's in my calc class, so here goes...

Eliminate the parameter t to find a Cartesian equation for:

x = t²
y = 5 + 3t
x = Ay² + By + C

where A = ??, B = ?? and C = ??

This is supposedly review, but I sure don't know what I'm doing here. Thanks in advance!

$\displaystyle \displaystyle \begin{align*} y &= 5 + 3t \\ y - 5 &= 3t \\ \frac{y - 5}{3} &= t \end{align*}$

Substitute this into $\displaystyle \displaystyle \begin{align*} x = t^2 \end{align*}$ and expand.

Ahh...I was looking for something like that but the more I stared at the problem the more frustrated I got. Thanks prove it! I'll finish solving it when I get home.

UPDATE: got it! I just needed to think it through the right way. A:1/9, B:-10/9, C: 25/9