Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
x = sqrt t
y = 1 - t
from first:
x = √t
so x^2 = t
from the second
t = 1-y
so x^2 = 1 - y
or
y = 1 - x^2 , a parabola
A polygon with 4 sides no two of wich need to be the same size
To eliminate the parameter and write the corresponding rectangular equation, we need to express one variable in terms of the other and then substitute it into the other equation.
Given:
x = √t
y = 1 - t
We can eliminate t by solving the first equation for t and then substituting it into the second equation:
From x = √t, we can square both sides to get rid of the square root:
x^2 = t
Now, substitute t = x^2 into the second equation:
y = 1 - (x^2)
This gives us the rectangular equation representing the curve:
y = 1 - x^2
The graph of this equation represents a downwards-opening parabola with its vertex at (0,1) and the axis of symmetry as the y-axis.