consider the following parametric equations:\n\n( x = sqrt { t + 4 } ) and ( y = 2 t + 5 )\n\nstep 1 of 2…

consider the following parametric equations:\n\n( x = sqrt { t + 4 } ) and ( y = 2 t + 5 )\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 + 4 } ) and ( y = 2 t + 5 )\n\nstep 1 of 2: eliminate the parameter ( t ). please write your answer in simplest form solved for ( y ).

Answer

Explanation:

Step1: Express (t) in terms of (x)

Given (x = \sqrt{t + 4}), square both sides: (x^{2}=t + 4), then (t=x^{2}-4).

Step2: Substitute (t) into the equation for (y)

Substitute (t=x^{2}-4) into (y = 2t+5). So (y=2(x^{2}-4)+5).

Step3: Simplify the equation

Expand (y = 2(x^{2}-4)+5): (y=2x^{2}-8 + 5). Then (y=2x^{2}-3). Since (x=\sqrt{t + 4}\geq0) (because the square root of a real - number (t + 4) is non - negative), the domain of (x) is (x\geq0).

Answer:

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