I'm taking calc this summer as an independent study. It's a stretch for me. So if I have a graph of a circle that has a radius of 3, the equation forthe circle is x squared + y squared = 9. Just wondering how the equation is obtained, since I can't seem to find the explanation in the book I'm using. If this is not the proper forum, then say so. Thanksdg
Equation of a graph.
- Thread starter Gobl0010
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The standard form of a circle is \(\displaystyle (x-h)^2+(y-k)^2=r^2\) where (h,k) is the center of the circle and r is the radius. The equation you describe would have the center at the origin (0,0), so then you get:
\(\displaystyle (x-0)^2+(y-0)^2=3^2\)
\(\displaystyle x^2+y^2=9\)
mmm4444bot
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It's been awhile, but I'm thinking that basic geometry and the Pythagorean Theorem were used to derive x^2 + y^2 = r^2. If you pick an arbitrary point on a circle centered at the origin (as long as the point is not on either axis), a right-triangle can be formed by connecting the point to the center and the x-axis.
Did you try googling?
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