Question

Explain how the pythagorean theorem is used to derive the equation of a circle

Answer 1

Its a bit tricky to explain without a diagram bot if we take a point (a, b) on the  coordinate plane as the center of the circle and another point (x,y) on the circumference then the distance between (a,b) and (x,y) is the radius of the circle. 

Now create a triangle  by drawing a line horizontally from (a,b) to the circumference and another line prerpendicular to this line from the point (x,y) to make a right angled triangl.e 

Applying the pythagoras theorem to this triangle gives

(x - a)^2 + (y - b)^2 = r^2  which is the standard form of equation of a circle.