Find a polar equation for the curve represented by the given Cartesian equation.

Question

Quizplus · Accepted Answer

The curve is represented by the Cartesian equation $y=x^2$, which can be rewritten as $r\sin	heta=(r\cos	heta)^2$. Simplifying using the identity $\sin^2	heta+\cos^2	heta=1$, we get $r=\frac{1}{\cos	heta}$, or $r^2=\frac{1}{\cos^2	heta}$. Multiplying both sides by $\frac{(\cos	heta)^2}{(\cos	heta)^2+\sin^2	heta}=1$, we get $r^2\cos^2	heta=1$, or $r=\frac{1}{\cos	heta}=sec	heta$. Converting to polar coordinates, we have $r=11eaa3e5_551f_8a0b_9f8f_bde131272cc4_{16}=sec	heta$.

Find a Polar Equation for the Curve Represented by the Given