Question

Find a set of parametric equations for y= -2x + 7, given the parameter t= √(x+4)

a) x=t^2-4 , y = -2(t^2-4) + 7
b) x=t^2+4 , y = -2(t^2+4) + 7
c) x=t^2-4 , y = -2t + 7
d) x=t^2+4 , y = -2t + 7

Answer 1

The correct set of parametric equations corresponding to y= -2x + 7 with parameter t= √(x+4) is x= t^2 - 4 and y= -2(t^2 - 4) + 7, which is option (a).

Step-by-step explanation:

To find a set of parametric equations for y= -2x + 7, given the parameter t= √(x+4), we should express both x and y in terms of t. Since t is defined as the square root of (x+4), we can square both sides to eliminate the square root, giving us t^2 = x + 4 or x = t^2 - 4. Substituting this x value into the original equation y = -2x + 7 gives us the y in terms of t: y = -2(t^2 - 4) + 7.

Therefore, the correct set of parametric equations is:

• x = t^2 - 4
• y = -2(t^2 - 4) + 7

This is an option (a).