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

Question

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

in progress 0
Natalia 10 hours 2021-11-25T12:04:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-25T12:05:19+00:00

    Answer:

    i put c

    Step-by-step explanation:

    0
    2021-11-25T12:05:21+00:00

    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

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )