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Agaiepsh

Answered question

2021-11-28

Find a set of parametric equations for the parabola whose equation is

y = 9 - x^{2}

Julie Mathew

Beginner2021-11-29Added 15 answers

Step 1
Given equation is,

y = 9 - x^{2}

Step 2
To find a set of parametric equations for the parabola whose equation is

y = 9 - x^{2}

The standard equation of parabola with center (h, k) is

{(x - h)}^{2} = 4 a (y - k)

And the parametric equations are

x = h + 2 a t, y = k + a t^{2}

The given equation

y = 9 - x^{2}

can be rewrite as

y - 9 = - {(x - 0)}^{2} \Rightarrow {(x - 0)}^{2} = - (y - 9)

Comparing

{(x - 0)}^{2} = - (y - 9)

with

{(x - h)}^{2} = 4 a (y - k)

get

(h, k) = (0, 9)

and

a = \frac{- 1}{4}

Thus the parametric equations are

x = 0 + 2 (\frac{- 1}{4}) t, y = 9 + (\frac{- 1}{4}) t^{2}

\Rightarrow x = \frac{- 1}{2} t, y = 9 - \frac{1}{4} t^{2}

Step 3
Therefore the parametric equation of the parabola

y = 9 - x^{2}

are

x = \frac{- 1}{2} t, y = 9 - \frac{1}{4} t^{2}

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