Question

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

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

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