Question

Consider the parametric equations below: x=√t ,y=7−t. Eliminate the parameter to find a Cartesian equation of the curve for x≥0. Which of the following represents the Cartesian equation of the curve?

A. x+y=7
B. x−y=7
C. x²+y=7
D. x²−y=7

Answer 1

To eliminate the parameter from the given parametric equations and find a Cartesian equation, square x to get t, then substitute it into y=7-t to get y=7-x². Rearranging yields the Cartesian equation x²-y=7.

Step-by-step explanation:

To eliminate the parameter and find the Cartesian equation of the curve for parametric equations x=√t, y=7−t with the condition x≥0, we can follow these steps:

1. First, note that since x is equal to the square root of t, t must be equal to x squared (t=x²).
2. Next, we substitute this expression for t into the second parametric equation for y, so we have y=7−x².
3. Finally, rearranging this equation, we get the Cartesian equation x²−y=7, which corresponds to choice D.

This equation represents a parabola that opens downwards since the coefficient in front of x² is positive and y is subtracted.