Question

What is the rectangular form of the parametric equations?What interval does x fall under?

Answer 1

Given:

`\begin{gathered} x\left(t\right)=t+6 \\ y(t)=4t^2-10 \end{gathered}`

Required:

To find the rectangular form of the parametric equations.

Step-by-step explanation:

x(t) = t+6

t = x(t) -6

Substitute this value of x in the equation

`\begin{gathered} y(t)\text{ =4t}^2-10 \\ y(t)=4(x(t)-6)^2-10 \\ y(t)\text{ = 4\lparen x\lparen t\rparen}^2-12x(t)+36)-10 \\ y(t)\text{ =4x\lparen t\rparen}^2-48x(t)+144-10 \\ y(t)\text{ = 4x\lparen t\rparen}^2-48x(t)+134 \end{gathered}`