SOLUTION: The shape of a state park can be modeled by a circle with the equation x^2+y^2=1600. A stretch of highway near the park is modeled by the equation y=1/40(x-40)^2. At what points do

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The shape of a state park can be modeled by a circle with the equation x^2+y^2=1600. A stretch of highway near the park is modeled by the equation y=1/40(x-40)^2. At what points do      Log On


   

Question 973700: The shape of a state park can be modeled by a circle with the equation x^2+y^2=1600. A stretch of highway near the park is modeled by the equation y=1/40(x-40)^2. At what points does a car on the highway enter or exit the park?
Found 2 solutions by lwsshak3, Alan3354:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The shape of a state park can be modeled by a circle with the equation x^2+y^2=1600. A stretch of highway near the park is modeled by the equation y=1/40(x-40)^2. At what points does a car on the highway enter or exit the park?
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Find the points of intersection of the two given equation
I don't know how to do it algebraically, but my graphic program shows entering the park from the left side at (0,40) and exiting the park on the right at (40,0)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The shape of a state park can be modeled by a circle with the equation x^2+y^2=1600. A stretch of highway near the park is modeled by the equation y=1/40(x-40)^2. At what points does a car on the highway enter or exit the park?
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Assuming you mean y+=+%281%2F40%29%2A%28x-40%29%5E2
x%5E2%2By%5E2=1600
Sub for y in the second equation:
x%5E2+%2B+%28%281%2F40%29%2A%28x-40%29%5E2%29%5E2+=1600
Multiply by 40^2
1600x%5E2+%2B+%28x-40%29%5E4+=+256000
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This gives a quartic, a 4th order equation.
Check for typos before trying to solve that.