Question

Describe full the graph that has the equation x^2 + y^2=9

Answer 1

see explanation

Explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 9 ← is in this form

with centre (0, 0 ) and r =
`√(9)` = 3

this then is the equation of a circle whose centre is (0, 0 ) with radius 3

Answer 2

Explanation:

Discussion

• First of all, the graph is of a circle. Anytime you see x^2 + y^2 = r^2, you are dealing with a circle
• The center is at 0,0. If it was anything else then x or y or both would be modified. (x+4)^2 + ( y - 3)^2 = 25 does not have it's center at 0,0
• Third, the radius of the circle is the square root of r^2. In this case, r^2 = 9 so r = sqrt(9) or r = 3