For the given parametric equations, find a corresponding x-y equation for the curve.

Question

Quizplus · Accepted Answer

From the given parametric equations, we can derive the following x-y equation:

x = t^2 - 1

y = t + 3

To eliminate the parameter t, we can solve the first equation for t:

t^2 = x + 1

Then substitute this expression for t^2 into the second equation:

y = sqrt(x + 1) + 3

or

y = -sqrt(x + 1) + 3

So the corresponding x-y equation for the curve is y = sqrt(x + 1) + 3 or y = -sqrt(x + 1) + 3.

Option C matches this equation.

For the Given Parametric Equations, Find a Corresponding X-Y Equation