Question

Find the center and the radius of the circle x^2 + y^2 +2x +6y =26

Answer 1

• Centre of the circle, (h,k)=(-1,-3)

,

• Radius = 6

Step-by-step explanation:

The standard form of the equation of a circle is:

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

Given the circle below:

`x^2+y^2+2x+6y=26​`

First, we reorder the terms.

`x^2+2x+y^2+6y=26​`

Next, we complete the square for the quadratics in x and y as shown below:

`\begin{gathered} x^2+2x+1^2+y^2+6y+3^2=26​+1^2+3^2 \\ (x+1)^2+(y+3)^2=36 \\ (x+1)^2+(y+3)^2=6^2 \end{gathered}`

Comparing with the standard form given above:

`\begin{gathered} h=-1 \\ k=-3 \\ \text{Centre of the circle, (h,k)=(-1,-3)} \\ \text{Radius, r=6} \end{gathered}`