Find an equation equivalent to r = 10 sin theta in rectangular coordinates.

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

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation:

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5