question\nwrite the parametric equations below as a rectangular equation by eliminating the…

question\nwrite the parametric equations below as a rectangular equation by eliminating the parameter.\n$x(t)=-7t^{2}+2$\n$y(t)=-4t - 8$

question\nwrite the parametric equations below as a rectangular equation by eliminating the parameter.\n$x(t)=-7t^{2}+2$\n$y(t)=-4t - 8$

Answer

Explanation:

Step1: Solve (y(t)=-4t - 8) for (t)

[ \begin{align*} y&=-4t - 8\ y + 8&=-4t\ t&=-\frac{y + 8}{4} \end{align*} ]

Step2: Substitute (t =-\frac{y + 8}{4}) into (x(t)=-7t^{2}+2)

[ \begin{align*} x&=-7\left(-\frac{y + 8}{4}\right)^{2}+2\ x&=-7\times\frac{(y + 8)^{2}}{16}+2\ x&=-\frac{7(y^{2}+16y + 64)}{16}+2\ x&=-\frac{7y^{2}+112y+448}{16}+2\ x&=-\frac{7y^{2}+112y + 448}{16}+\frac{32}{16}\ x&=\frac{-7y^{2}-112y - 416}{16} \end{align*} ]

Answer:

(x=\frac{-7y^{2}-112y - 416}{16})