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eliminate the parameter tt to find a cartesian equation for: x=t2andy=9 4t. x=t2andy=9 4t. and express your equation in the form x=ay2 by c.

User Chadams
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1 Answer

6 votes

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.

User Alpha Huang
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