Convert the polar equation to a rectangular equation. r = -9 cos theta

heelallev5 2022-08-05 Answered
Convert the polar equation to a rectangular equation.
r = 9 cos θ
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Answers (2)

Nicole Soto
Answered 2022-08-06 Author has 10 answers
r = x 2 + y 2 and x = r cos θ cos θ = x r
r = 9 cos θ = 9 x r
r 2 = 9 x
x 2 + y 2 = 9 x
( x + 9 2 ) 2 + y 2 = 81 4 Completing the square
( x + 9 2 ) 2 ( 9 2 ) 2 + y 2 ( 9 2 ) 2 = 1 Equation of an ellipse
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ghettoking6q
Answered 2022-08-07 Author has 8 answers
Given the polar equation
r = 9 cos θ
Multiply both sides of the equation by r.
r 2 = 9 cos θ
Use the following conversions: r 2 = x 2 + y 2 , x = r cos θ.
x 2 + y 2 = 9 x
Add 9x to both sides of the equation.
( x 2 + 9 x ) + y 2 = 0
Complete the square.
( x 2 + 9 x 81 4 ) + y 2 = 81 4
( x + 9 2 ) 2 + y 2 = 81 4 ....Rectangular Equation
Conic Section is a Circle
center: (h, k)------(-9/2, 0)
radius (r): 9/2
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