Question

Find a polar equation for the curve represented by the given Cartesian equation. (Use t in lieu of θ in your answer.) x2+y2=8cx

Answer 1

Answer:

The polar equation of the curve is:

$r=8c*cos(\theta)$

Step-by-step explanation:

In polar form x and y could be written as:

$x=rcos(\theta)$

$y=rsin(\theta)$

Taking the square of each value we have:

Let's recall that $cos^{2}(\theta)+sin^{2}(\theta)=1$

$x^{2}+y^{2}=r^{2}(cos^{2}(\theta)+sin^{2}(\theta))$

$x^{2}+y^{2}=r^{2}$

Then, the cartesian equation is rewritten as:

$x^{2}+y^{2}=8cx$

$r^{2}=8c*rcos(\theta)$

Therefore, the polar equation of the curve is:

$r=8c*cos(\theta)$

I hope it helps you!