Convert the parametric equations 𝑥
equals 𝑡 squared plus two and 𝑦 equals three 𝑡 minus one to rectangular form.
Here, we have a pair of parametric
equations. We have 𝑥 is equal to some
function of 𝑡 and 𝑦 is equal to some other function of 𝑡. To convert parametric equations to
rectangular form, we need to find a way to eliminate the 𝑡. So looking at our equations, we can
see that we can rearrange the equation in 𝑦 to make 𝑡 the subject. We begin by adding one to both
sides. And then, we divide through by
three. So we see that 𝑡 is equal to 𝑦
plus one all over three.
Now, we go back to our equation for
𝑥. We replace 𝑡 with 𝑦 plus one over
three. And we find that 𝑥 equals 𝑦 plus
one over three all squared plus two. And there will be certain
circumstances where we’re required to distribute the parentheses and simplify. In this case, that’s not
necessary. And so, we’re finished. We’ve converted the parametric
equations 𝑥 equals 𝑡 squared plus two and 𝑦 equals three 𝑡 minus one into
rectangular or Cartesian form. It’s 𝑥 equals 𝑦 plus one over
three all squared plus two.