- Thread starter Illvoices
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That form of the equation of a circle is just an expression of the distance formula.

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Is that the question you've got, or are you starting with a second question?… I've got a question … I start by asking where is the science …

I'm not sure what you're thinking about science. Can you post an example?

That plus sign is a typo.(x - h)^{2}+ (y+k)^{2}= r^{2}

(x - h)

The circle's center is the point (h, k).

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If you are asking "Why is that the equation of a circle", then you have to specify that you are representing x and y in a "Cartesian coordinate system" where the x and y axes are at

All the points on a circle with center at (0, 0) and radius r have distanced r from (0,0) (pretty much the definition of "circle") so \(\displaystyle r= \sqrt{x^2+ y^2}\) and. squaring both sides, \(\displaystyle r^2= x^2+ y^2\).