Answer:
Step-by-step explanation:
The equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We have our h and k from the center as h = -1 and k = -3, and we also know the radius, which is 6. We also have an x/y coordinate as (-6, -6) and we want to know if that coordinate lies in, on, or outside of the circle. The way we will do that is plug everything into the circle equation and solve. If what we solve for is less than the radius, then the point is inside the circle; if what we solve for is equal to the radius, then the point is on the circle; if what we solve for is greater than the radius, then the point in outside the circle. Here we go:
[tex](-6-(-1))^2+(-6-(-3))^2?36[/tex] . There's a question mark there intentionally. The left side is the one we are solving for to see if it is less than, equal to, or greater than, 36. Continuing,
[tex](-6+1)^2+(-6+3)^2? 36[/tex] and
[tex](-5)^2+(-3)^2?36[/tex] and
25 + 9 ? 36
34 ? 36
We know that 34 is less than 36, so the point lies INSIDE the circle.
