What is the equation of the circle with the center at the origin and with a radius of 9?
a.)x^2 + y^2 = 81
b.)(x - 1)^2 + (y - 1)^2 = 18
c.)x^2 + y^2 = 18
I'm pretty sure the answer is: x^2 + y^2 = 81
You are right
Thanks:)
What if the 9 was 6?
Yes, you are correct. The equation of a circle with the center at the origin (0, 0) and a radius of 9 is indeed x^2 + y^2 = 81.
To understand why this is the case, let's break it down:
The general equation of a circle can be written as (x - a)^2 + (y - b)^2 = r^2, where (a, b) represents the center of the circle and r represents the radius.
In this case, the center of the circle is at the origin (0, 0). So, the equation becomes (x - 0)^2 + (y - 0)^2 = r^2, which simplifies to x^2 + y^2 = r^2.
Since the radius is given as 9, we substitute r with 9 in the equation, resulting in x^2 + y^2 = 81.
Out of the given options, x^2 + y^2 = 81 (option a) is the equation that satisfies the conditions of a circle with the center at the origin and a radius of 9.