How is the Pythagorean Theorem used to develop the equation of a circle in standard form?

Question

I have no clue nor do I have any idea where to find the answer.

Answer 1

Say a circle has centre (a,b) and radius r. Take any point on the circle with coordinate (x,y) and join it to the centre of the circle. Use vertical and horizontal lines to complete a right-angled triangle. Its horizontal side will be (x - a) and its vertical side will be (y - b). Using pythagoras we get (x - a)^2 + (y - b)^2 = r^2

Answer 2

Inside the circle, you can fit a right triangle in there. This means you have a locus of points that describes a right triangle that is also a locus of points that describes a circle.

The theorem is c^2 = a^2 + b^2 and the equation of a circle is r^2 = x^2 + y^2. Do you see the similarity? Thus, the connection.

Answer 3

the formula of a circle is x^2 + y^2 = r^2, where r is radius. this _is_ the pythagorean theorem. the best way to see it is to solve for y( y = +/- sqrt( r^2 - x^2) and graph it. you will see a circle. hope this helps.