Find a set of parametric equations for y= -4x + 9 given the parameter t= Sqrt x-1.

Question

Answer choices:
A) x(t) =t^2 + 1
y(t) =-4t^2 + 5

B) x(t)= t^2 - 1
y(t) =-4t^2 + 5

C) x(t) =t^2 + 1
y(t) =-4t^2 + 13

D) x(t) =t^2 -1
y(t) =-4t^2 + 13

Thanks!

Answer 1

If

t = √ ( x -1 )

then

t² = [ √ ( x -1 ) ]²

t² = x - 1

Add 1 to both sides

t² + 1 = x

x = t² +1

Put this value in equation:

y = - 4 x + 9

y = - 4 ( t² +1 ) + 9

y = - 4 t² - 4 + 9

y = - 4 t² + 5

Answer A