Question

Describe the region enclosed by the circle x^2 +y^2 = 11x in polar coordinates.

Answer 1

Answer:

the region of the circle in polar coordinate can be expressed as:

$\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}$

Step-by-step explanation:

Given that:

$x^2 +y^2 = 11x$

This implies that :

$(x-5.5)^2 + y^2 = 5.5^2$

center (5.5, 0) and radius = 5.5

The relation between the cartesian coordinates (x,y) and the polar coordinates (r, θ) is as follows:

x = rcosθ

y = rsinθ

Thus, $x^2 + y^2 = r^2$

$x^2 + y^2 = 11x$

$(rcos \theta)^2 + (r sin \theta)^2 = 11(rcos \theta)$

$r^2 = 11r cos \theta$

Thus, the angle θ runs between $- \dfrac{\pi}{2}$ to $\dfrac{\pi}{2}$

Therefore, the region of the circle in polar coordinate can be expressed as:

$\mathbf{- \dfrac{\pi}{2} \leq \theta \leq \dfrac{\pi}{2} , 0 \leq r \leq 11 cos \theta}$