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?
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Assuming you mean {{{y = (1/40)*(x-40)^2}}}
{{{x^2+y^2=1600}}}
Sub for y in the second equation:
{{{x^2 + ((1/40)*(x-40)^2)^2 =1600}}}
Multiply by 40^2
{{{1600x^2 + (x-40)^4 = 256000}}}
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This gives a quartic, a 4th order equation.
Check for typos before trying to solve that.