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Write the radius of the circle write your answer in simplified, rationalized form

Write the radius of the circle write your answer in simplified, rationalized form-example-1
User Garnett
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1 Answer

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The equation of the circle given is,


x^2+y^2+36-15y=0

Move 36 to the right hand side


\begin{gathered} x^2+y^2-15y=-36+0 \\ x^2+y^2-15y=-36 \end{gathered}

Complete the square on y


\begin{gathered} x^2+(y^2-(15)/(2)y+((-15)/(2))^2)=-36+(-(15)/(2))^2 \\ x^2+(y^2-(15)/(2)y+(225)/(4))=-36+(225)/(4) \\ x^2+(y-(15)/(2))^2=(81)/(4) \end{gathered}

The general form of the equation of a circle at the origin is,


x^2+y^2=r^2

Comparing the equation given and the general form of the equation


r^2=(81)/(4)

Simplify


\begin{gathered} r=\sqrt{(81)/(4)}=(9)/(2) \\ \therefore r=(9)/(2)\text{ or 4.5} \end{gathered}

Hence, the answer is


r=(9)/(2)\text{ or 4.5}

User JanPl
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