Question

Which graph represents the parametric equations 

x = t – 4

y = t² + 5

–1 ≤ t ≤ 2

Answer 1

Given:

$x=t-4\\y=t^2+5$

So to find equation of the curve we start with y,

and using a basic conversion in the given equation,

$y=t^2+5\\y=t^2+5-16+16 \\y=(t^2-16)+21 \\y=(t-4)(t+4)+21 \\y=(t-4)(t-4+8)+21$

Now putting,

$x=t-4$

we further get,

$y=x(x+4)+21 \\y=x^2+8x+21$ .............is the required curve. Now plotting on the graph

–1 ≤ t ≤ 2

we get,

This graph represents the given parametric equations.