Question

The equation of a circle is given below. Identify the radius and the center. Then graph the circle.4x² + 4y2 - 8y-117 = 0

Answer 1

the Given:

`4x^2+4y^2-8y-117=0`

Express the equation into standard form,

`\begin{gathered} 4x^2+4y^2-8y-117=0 \\ 4x^2+4y^2-8y=117 \\ x^2+y^2-2y=(117)/(4) \\ x^2+y^2-2y+1=(117)/(4)+1 \\ (x-0)^2+(y-1)^2=(121)/(4) \\ (x-0)^2+(y-1)^2=((11)/(2))^2 \end{gathered}`

Compare it with standard form of the equation of a circle,

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (h,k)=\text{center} \\ r=\text{radius} \end{gathered}`

It gives,

Center = (0,1)

Radius = 11/2