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

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

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

Answer

Explanation:

Step1: Solve for (t) from the equation 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 of (y)

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

Step3: Simplify the expression for (y)

Expand the right - hand side: (y = 2x^{2}-8 + 5). Then (y=2x^{2}-3). Also, note that since (x=\sqrt{t + 4}), (x\geq0).

Answer:

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