Write the polar equation in rectangular form. r = 6 sin θ

y = –6x

y = x – 3

x2 + (y – 3)2 = 9

(x – 3)2 + y2 = 9

The rectangular form of the polar equation is x² + (y - 3)² = 9 ⇒ 3rd answer

Step-by-step explanation:

The graph of the polar equation r = a sin Ф is a circle where

∵ The polar equation is r = 6 sin Ф

- That means the graph of the equation is a circle

∴ The polar equation represents a circle

∵ a = 6

∵ The coordinates of the center of the circle are (0 , a/2)

∵ 6 ÷ 2 = 3

∴ The coordinates of the center of the circle are (0 , 3)

∵ The coordinates of the center of the circle are (h , k)

∴ h = 0 and k = 3

∵ The length of the diameter of the circle = a

∴ The length of the diameter of the circle = 6

- The length of the radius of the circle is half to the length

    of the diameter

∴ The length of the radius = × 6 = 3

∴ r = 3

- Substitute the values of h, k and r in the rectangular form of

   the equation of the circle

∵ (x - 0)² + (y - 3)² = (3)²

∴ x² + (y - 3)² = 9

The rectangular form of the polar equation is x² + (y - 3)² = 9

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.