Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
x = sqrt t
y = 1 - t
x^2 = t
so by substitution
y = 1-x^2
A PARABOOLA
YAY
To eliminate the parameter, we can solve for t in terms of x from the first equation and substitute it into the second equation.
Let's start with the first equation, x = √t. To get t by itself, we need to square both sides of the equation:
x² = (√t)²
x² = t
Now we have t in terms of x. We can substitute this expression into the second equation, y = 1 - t:
y = 1 - x²
Therefore, the corresponding rectangular equation is y = 1 - x². The graph of this equation represents the curve.