Given:
[tex]\begin{gathered} x\left(t\right)=t+6 \\ y(t)=4t^2-10 \end{gathered}[/tex]
Required:
To find the rectangular form of the parametric equations.
Explanation:
x(t) = t+6
t = x(t) -6
Substitute this value of x in the equation
[tex]\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}[/tex]
