Answer:
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 coordinates of the center of the circle is (0 , a/2)
- The length of the diameter of the circle is equal to a
- The rectangular form of the equation of a circle is (x - h)² + (y - k)² = r², where h and k are the coordinates of its center and r is its radius
∵ 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 = [tex]\frac{1}{2}[/tex] × 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
