Question

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

Answer 1

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}`