Question

Which points are on a plane curve described by the following set of parametric equations?

Answer 1

ANSWER

The points (1,2) and (7,2) lie on the given curve.

EXPLANATION

The given parametric equations are:

$x = 3t + 4$

and

$y = 2 {t}^{2}$

We make t the subject in the first equation to obtain:

$t = \frac{x - 4}{3}$

We substitute this into the second equation to get:

$y =2{(\frac{x - 4}{3} )}^{2}$

When x=1,

$y = 2 {(\frac{1 - 4}{3} )}^{2} = 2$

When x=2

$y =2{(\frac{2- 4}{3} )}^{2} = \frac{8}{9}$

When x=7,

$y =2{(\frac{7 - 4}{3} )}^{2} = 2$

Therefore the points (1,2) and (7,2) lie on the given curve.