Question

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

Answer 1

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)

Answer 2

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