A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t= the square root

Question

3 years ago

5

A class is trying to eliminate t from the parametric equations x=t^2+3 and y=4t. Beth says that she can write t= the square root

of (x-3) to eliminate the parameter. Why is this wrong?
A)She should have added 3 to x, not subtracted.
B)She should always solve for t as a function of y.
C)She should have taken both the positive and negative square root.
D)She should first substitute y for t before solving.

I think it might be C, but I'm not sure.

Mathematics

1 answer:

luda_lava [24] · Answer 1 · 2022-07-19T19:34:59+03:00

The answer
<span>to eliminate t from the parametric equations x=t^2+3 and y=4t
we have t²= x-3, and then t= sqrt(x-3), but we know that y=4t, which implies t=y/4. We only substitute the value of t by y/4, so </span>t= sqrt(x-3) wich is equivalent to y/4=sqrt(x-3), so at last y= 4 sqrt(x-3). t exactly eliminated.
so the true answer is
<span>D)She should first substitute y for t before solving.</span>