Answer:
r = 10sinθ
Is
x² + (y - 5)² = 25
in rectangular coordinates.
Step-by-step explanation:
To convert r = 10sinθ to rectangular coordinates,
First, note the following equivalents
r² = x² + y²
x = rcosθ
y = rsinθ
=> sinθ = y/r
Now, r = 10sinθ
Implies
r = 10 × y/r
Multiply both sides by r
r² = 10y
Since r² = x² + y², we have
x² + y² = 10y
Or
x² + y² - 10y = 0
Completing the square for y² - 10y, we have
x² + [y² -2(5)y + 5² - 5²] = 0
x² + (y - 5)² - 25 = 0
x² + (y - 5)² = 25
Centered at (0, 5) with radius 5
