Question

Find a polar equation for the curve represented by the given Cartesian equation. x^{2}+y^{2}=100

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asked 2021-05-13
Find a polar equation for the curve represented by the given Cartesian equation.
\(x^{2}+y^{2}=100\)

Answers (1)

2021-05-14
Step 1
Here given cartesian equation
\(x^{2}+y^{2}=10^{2}\)
it is an equation of the circle with radius 10.
Step 2
Put
\(x=r\cos 0\)
\(y=r\sin 0\)
Thus
\((r\cos 0)^{2}+(r\sin 0)^{2}=100\)
\(r^{2}(\cos^{2} 0+\sin^{2} 0)=100\)
\(r^{2}=100\)
\(r=\pm 10\)
Thus the polar equation of the circle is
r = 10 or r = - 10
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