consider the following parametric equations:\n\n( x = sqrt { t - 2 } ) and ( y = 3 t + 1 )\n\nstep 1 of 2…

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

Answer

Explanation:

Step1: Solve (x = \sqrt{t - 2}) for (t)

Square both sides: (x^{2}=t - 2), then (t=x^{2}+2).

Step2: Substitute (t) into (y = 3t+1)

Substitute (t=x^{2}+2) into (y = 3t + 1): (y=3(x^{2}+2)+1).

Step3: Simplify the expression

Expand and simplify: (y = 3x^{2}+6 + 1=3x^{2}+7). Since (x=\sqrt{t - 2}\geq0), the domain of (x) is (x\geq0).

Answer:

(y = 3x^{2}+7,x\geq0)