Question

What is a radius of a circle whose equation is x^2+y^2=9

Answer 1

What is the definition of a circle?

Answer 2

the equation of center (0,0) with raduis r
has the equation of :-
\( x^2+y^2=r^2\)

Answer 3

@ikram002p is right. Here is how you get that:

A circle is defined as all the points in a plane that are the same distance from a given point in the plane.

Now given the point (0,0), what is the distance r to an arbitrary point (x, y)?

The difference in the first coordinate (abscissa) values is x-0. That is the length of one leg of a right triangle. The difference in the the second coordinates is the length of the other leg of a right triangle, so thanks to Pythagoras the distance between the arbitrary point (x, y) and the origin is:

\[\large r = \sqrt{(x-0)^2 + (y-0)^2} = \sqrt{{x^2+y^2}}\]

Squaring both sides:

\[\large r^2 = x^2+y^2\]