Question

how does x^2+y^2 equal a circle? It only equals the radius so how does that have anything to do with actually drawing the circle. Everything I read about, only shows you how to get the radius of the circle and nothing to do with actually getting the circle. Like a 2π would be nice somewhere but there's nothing! Please help!

Answer 1

The standard form of the equation of a circle is given as:

`(x-a)^2+(y-b)^2=r^2`

The coordinate point (a,b) is the center of the circle.

The value, r is the radius of the circle.

For the given equation:

`x^2+y^2=r^2`

This can be rewritten as:

`(x-0)^2+(y-0)^2=r^2`

This simply implies that the circle with the given equation has a center at the point (0,0), origin, and has a radius of r units.

Take for example the equation of a circle:

`x^2+y^2=25`

Rewrite the equation in standard form:

`(x-0)^2+(y-0)^2=5^2`

Compared with the general form given, it follows that a=0, b=0, and r=5.

It follows that the center of the circle is (0,0) and its radius is 5 units.

Note that this information was derived from the equation of the circle, which can then be used to graph the circle.

Plot the center (0,0) and then draw a circle with a radius of 5 units using the center.

So all you need do to draw the circle is to locate the center point (0,0) and then draw a circle with radius, r using the center.