My teacher wants me to figure out how the Pythagorean Theorem and the Equation of a Circle are related. I can't figure this out because I view them as being two completely different things. I understand what the equation for a circle is, but how does that relate to the Pythagorean Theorem?
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$\begingroup$Draw a circle with radius $r$ and center at the origin. In polar coordinates, $x=r\sin \theta,y=r\cos\theta$. $x^2+y^2=1$ is thus true.
The equation for a circle is $(x-a)^2 + (y-b)^2 = r^2$. You can use the following diagram: 
$$(x−a)^2+(y−b)^2=r^2$$
Look at the equation of a circle with center $(a,b)$ and radius $r$.
Consider the right triangle with sides $A = x-a, B = y-b$ and $C = r$. You see that the equation of the circle is just the Pythagorean theorem.
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