Question

What does x ^2 + y^2 = 9 mean? What about x ^2 + y ^2 = 0 ? Can a circle have a radius of − 3 ? Why or why not?

Answer 1

`x ^(2) + {y}^(2) = r^(2)`

since all the terms are squared so there can be a negative number

but in number line

...... -4,-3,-2,-1,0,1,2,3.......

as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.

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`{x}^(2) + {y}^(2) = 9`

it means the origin is (0,0) and radius 3

Answer 2

See below.

Explanation:

Compare our equation with one standard form of a circle:

x^2 + y^2 = r^2 where r = the radius.

So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.

x^2 + y^2 = 0 is not a circle because r = 0 ( a radius of 0). A circle of radius 0 is really a point!!

The value of the radius of a circle must be positive so it cannot have a radius of -3.