Answer:
Explanation:
To eliminate the parameter t and find a Cartesian equation for the parametric equations x = t^2 and y = 9 - 4t, we can solve the first equation for t and substitute it into the second equation.
From x = t^2, we can solve for t as t = √x.
Substituting this value of t into the equation y = 9 - 4t, we get y = 9 - 4√x.
To express the equation in the form x = ay^2 + by + c, we need to manipulate the equation further.
Rearranging the equation y = 9 - 4√x, we have √x = (9 - y)/4.
Squaring both sides to eliminate the square root, we get x = ((9 - y)/4)^2.
Expanding and simplifying further, we have x = (81 - 18y + y^2)/16.
Therefore, the Cartesian equation for the parametric equations x = t^2 and y = 9 - 4t, expressed in the form x = ay^2 + by + c, is:
x = (81 - 18y + y^2)/16.