Convert the polar equation to a rectangular equation. r = − 9 cos ⁡ θ

Question

Convert the polar equation to a rectangular equation.  r  =  −  9  cos  ⁡  θ

Nicole Soto · Accepted Answer

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

ghettoking6q · Accepted Answer

Given the polar equation  r  =  −  9  cos  ⁡  θMultiply both sides of the equation by r.      r          2        =  −  9  cos  ⁡  θUse the following conversions:       r          2        =      x          2        +      y          2        ,  x  =  r  cos  ⁡  θ.      x          2        +      y          2        =  −  9  xAdd 9x to both sides of the equation.  (      x          2        +  9  x  )  +      y          2        =  0Complete the square.  (      x          2        +  9  x      81    4    )  +      y          2        =      81    4    (  x  +      9    2        )          2        +      y          2        =      81    4  ....Rectangular EquationConic Section is a Circlecenter: (h, k)------(-9/2, 0)radius (r): 9/2

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

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