Rewrite the parametric equation by eliminating the parameter x=4t+1 and y=t-3

Question

Rewrite the parametric equation by eliminating the parameter x=4t+1 and y=t-3

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Peyton 6 days 2021-10-11T19:23:24+00:00 1 Answer 0

Answers ( )

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    2021-10-11T19:25:02+00:00

    Answer:

    The equation is x = 4y + 13

    Step-by-step explanation:

    * Lets talk about the parametric equations

    – Parametric equations are a set of equations that express a set

     of quantities as explicit functions of a number of independent

     variables

    – Ex: x = at + b and y = ct + d are parametric equations

    – We use them to find relation between the variables x and y

    * Lets solve the problem

    ∵ x = 4t + 1 ⇒ (1)

    ∵ y = t – 3 ⇒ (2)

    – The parameter is t to eliminate it find t in terms of x or y

    – We will use equation (2) to find t in terms of y

    ∵ y = t – 3 ⇒ add 3 to both sides

    ∴ t = y + 3 ⇒ (3)

    – Substitute the value of t in equation (3) in equation (1)

    ∵ x = 4t + 1

    ∵ t = y + 3

    ∴ x = 4(y + 3) + 1 ⇒ open the bracket

    ∴ x = 4y + 12 + 1 ⇒ add like term

    ∴ x = 4y + 13

    * The equation is x = 4y + 13

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