Question

What is the general form of the equation of a circle with a center at the origin and a radius of 9?

Answer 1

`x^2+y^2=81`

Explanation:

Any general circle centred at `(a,b)` and with radius `r` has equation `(x-a)^2+(y-b)^2=r^2`

So in this case since the centre is the origin, it implies that `a=b=0`, and the radius `r=9 => r^2=9^2=81`.

Thus the equation reduces to `x^2+y^2=81`.

Answer 2

`x^2 + y^2 = 9^2`

Explanation:

General Equation of a circle:
`(x-a)^2+(y-b)^2=r^2`
where (a,b) are the coordinates of center and 'r' is the radius
since in you question center lies on origin and the radius is 9
therefore, (a,b) = (0,0) and r=9
hence, `x^2 + y^2 = 9^2`