Question

Is my answer correct and how do you know? I just graphed it , is there another way I could do it?

Answer 1

yes and yes,

the equation of a circle with a center at (h,k) with a radius of "r" is

`(x-h)^2 +(y-k)^2=r^2`

you know the center (h,k) is (-3,1) and r= 10, so you could plug in the answers and see which ones will match

A more intuitive method of doing it is to recognize that the given equation is like the pythagorean theorem. Also, know that a 3-4-5 is a right triangle and thus a 6-8-10 is also a right triangle.
since radius is 10, that means the other 2 values (x-x1) and (y-y1) must be equal to 6 and 8, so find the answer that will give yuo 6 and 8

Answer 2

Note the general equation of a circle is x^2 + y^2 = r^2, with centre (0, 0) and radius: r.

So, our equation of a circle is (x + 3)^2 + (y - 1)^2 = 100

Subtract 100 from both sides and plug in the points. If it equals to 0, then the points satisfy the equation of the circle (ie lies on the circle)