Question

Consider the following parametric equation. x equals (t plus 5 )squared​; y equals t plus 8​; negative 10 less than or equals t less than or equals 10 ​(a) Eliminate the parameter to obtain an equation in x and y. ​(b) Describe the curve and indicate the positive orientation. ​(a) Eliminate the parameter to obtain an equation in x and y. Choose the correct equation below. A. y equals StartRoot x plus 3 EndRoot B. y equals (x plus 3 )squared C. y equals x squared plus 3 D. y equals 3 plus or minus StartRoot x EndRoot ​(b) Describe the curve and indicate the positive orientation. A. -15 15 -5 15 x y

Answer 1

a) D. y = 3 ±√x

b) parabola opening to the right

Explanation:

(a) Solving for t in the equation for y:

y = t+8

t = y -8 . . . . subtract 8

Substituting into the equation for x, we have ...

x = ((y -8) +5)^2 = (y -3)^2

Solving for y, we get

±√x = y -3 . . . . . take the square root

y = 3 ±√x

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(b) The equation describes a parabola that opens to the right.