The polar equation r^2 - 2r(sin q) = 3 corresponds to which, of the rectangular equations listed.?

Question

The polar equation r^2 - 2r(sin q) = 3 corresponds to which, of the rectangular equations listed.

possible answers to choose from....

a. (x + 1)^2 + (y + 1)^2 = 4
b. (x + 1)^2 + (y - 1)^2 = 4
c. (x - 1)^2 + (y + 1)^2 = 4
d. (x - 1)^2 + (y - 1)^2 = 4
e. x^2 + (y + 1)^2 = 4
f. x^2 + (y - 1)^2 = 4
g. (x + 1)^2 + y^2 = 4
h. (x - 1)^2 + y^2 = 4
i. none of these

Answer 1

Remember the identities.

x = rcos(q)
y = rsin(q)
x² + y² = r²

Now take the equation and convert it.

r² - 2rsin(q) = 3

x² + y² - 2y = 3
x² + (y² - 2y + 1) = 3 + 1
x² + (y - 1)² = 4

The answer is f.

Answer 2

the oblong equation (x - 2)² + y² = 4 corresponds to which of the polar equations listed decrease than? bear in suggestions the identities: x = rcos? y = rsin? x² + y² = r² cos²? + sin²? = a million _______ (x - 2)² + y² = 4 Plug interior the polar equivalents. (rcos? - 2)² + (rsin?)² = 4 r²cos²? - 4rcos? + 4 + r²sin²? = 4 r²cos²? + r²sin²? = 4rcos? r²(cos²? + sin²?) = 4rcos? r² = 4rcos? Divide via r. r = 4cos? considering the fact that it is not a call the respond is i. none of those

Answer 3

it's sooo complicated!! ^_^V

ours dont have sines and cosines... haha.. im sorry im not capable of helping you..