Question Video: Converting Parametric Equations into Rectangular Form Mathematics • 12th Grade

Convert the parametric equations π₯ = βπ‘ and π¦ = 5π‘β΄ + 4π‘ to rectangular form.

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Video Transcript

Convert the parametric equations π₯ is equal to the square root of π‘ and π¦ is equal to five π‘ to the fourth power plus four π‘ to rectangular form.

Weβre given a pair of parametric equations. And weβre asked to convert these into the rectangular form. Recall, this means we need to convert this into an equation involving just π₯ and π¦. We need to eliminate the variable π‘. And thereβs lots of different methods we can try for different types of parametric equations. Usually, the best way to start is to take a look at our parametric equations.

In this instance, we can see π₯ is equal to the root of π‘ and π¦ is equal to five π‘ to the fourth power plus four π‘. And we want to eliminate the variable π‘ from this expression. And we can see that π₯ is equal to the root of π‘. We could just substitute this into our expression for π¦. Recall, if π¦ is five π‘ to the fourth power plus four π‘, then we can replace π‘ in this expression with the square root of π‘ squared. So π¦ is equal to five times root π‘ all squared all raised to the fourth power plus four times root π‘ all squared.

But remember, root π‘ is equal to π₯. So we could replace each of these expressions of root π‘ with π₯. Doing this gives us five times π₯ squared all raised to the fourth power plus four π₯ squared. Then we can simplify this. By using our laws of exponents, π₯ squared all raised to the fourth power is equal to π₯ to the power of two times four. And then we can evaluate this to give us our final answer: π¦ is equal to five π₯ to the eighth power plus four π₯ squared.

Therefore, we were able to convert the parametric equations π₯ is equal to root π‘ and π¦ is equal to five π‘ to the fourth power plus four π‘ to the rectangular form. We got π¦ is equal to five π₯ to the eighth power plus four π₯ squared.