Math CentralQuandaries & Queries


Question from Balraj, a student:

I have to draw a circle x^2+y^2 =8x . please tell me how to understand these coordinates ? please elaborate , on how to understand these types of equations.

Hi Balraj,

The equation of the circle with centre $(h, k)$ and radius $r$ is

\[(x - h)^2 + (y - k)^2 = r^2 .\]

To put your equation in this form add $-8 x$ to each side to get

\[x^2 - 8x + y^2 = 0 .\]

To complete the square of $x^2 - 8x$ you need to add $16$ so add $16$ to each side of the equation and display the result in the form

\[(x - h)^2 + (y - k)^2 = r^2 .\]


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