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Find an equation equivalent to r=5/1+cos0 in rectangular coordinates

A. x^2=25-10y
B. X^2=10y-25
C.y^2=10x-25
C. Y^2= 25-10x

User Donstack
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1 Answer

1 vote


r=\frac5{1+\cos\theta}\implies r(1+\cos\theta)=5\implies r+r\cos\theta=5

In converting between polar and rectangular coordinates, we take


x^2+y^2=r^2\implies r=√(x^2+y^2)


x=r\cos\theta

so that the equation becomes


√(x^2+y^2)+x=5

which we can rewrite as


√(x^2+y^2)=5-x


x^2+y^2=(5-x)^2


x^2+y^2=25-10x+x^2


\implies\boxed{y^2=25-10x}

so the answer is C.

User Sahil Agarwal
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7.3k points