Question Video: Convert Parametric Equations to Rectangular Form | Nagwa Question Video: Convert Parametric Equations to Rectangular Form | Nagwa

# Question Video: Convert Parametric Equations to Rectangular Form Mathematics • Higher Education

Convert the parametric equations π₯ = ln (1/2 π‘) and π¦ = 3π‘Β² to rectangular form.

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### Video Transcript

Convert the parametric equations π₯ equals ln of a half π‘ and π¦ equals three π‘ squared to rectangular form.

In order to convert these parametric equations into rectangular form, we need to eliminate the variable π‘. So, weβre left with an equation containing π¦ and π₯ only. Letβs consider the equation. [π₯] is equal to ln of a half π‘ and rearrange it to make π‘ the subject. To eliminate the ln from the right-hand side, we put both sides as a power of π. On the right-hand side, the π and ln cancel so that π to the power of π₯ is equal to a half π‘. Our final step is to multiply both sides by two. Two π to the power of π₯ is equal to π‘.

Letβs now consider our second equation π¦ equals three π‘ squared. As π‘ is equal to two π to the power of π₯, we can substitute this into the equation. This gives us three multiplied by two π to the power of π₯ squared. Two π to the power of π₯ multiplied by two π to the power of π₯ is equal to four π to the power of two π₯. Remember, when multiplying, we can add our exponents or indices.

Our equation simplifies to π¦ is equal to three multiplied by four π to the power of two π₯. Three multiplied by four is equal to 12. So, π¦ is equal to 12π to the power of two π₯. We now have our equation in rectangular form by eliminating the variable π‘ and leaving our final equation in terms of π¦ and π₯.

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