consider the following parametric equations:\n\n$x = \\frac{t}{-3}$ and $y = t^{2}-3$\n\nstep 1 of 2…

consider the following parametric equations:\n\n$x = \\frac{t}{-3}$ and $y = t^{2}-3$\n\nstep 1 of 2: eliminate the parameter $t$. please write your answer in simplest form solved for $y$.

consider the following parametric equations:\n\n$x = \\frac{t}{-3}$ and $y = t^{2}-3$\n\nstep 1 of 2: eliminate the parameter $t$. please write your answer in simplest form solved for $y$.

Answer

Explanation:

Step1: Solve for ( t ) from ( x ) equation

Given ( x=\frac{t}{-3} ), multiply both sides by (-3) to get ( t=-3x ).

Step2: Substitute ( t ) into ( y ) equation

Substitute ( t = - 3x ) into ( y=t^{2}-3 ). Then ( y=(-3x)^{2}-3 ). Simplify ( (-3x)^{2}-3 ): Using the formula ((ab)^2=a^{2}b^{2}), ((-3x)^{2}=(-3)^{2}x^{2}=9x^{2}). So ( y = 9x^{2}-3 ).

Answer:

( y=9x^{2}-3 )