Let's first determine the equation for the circle in question. If the center is at the origin, then the h and k values are both 0. If the radius is 5, we can write the equation for the circle as [tex]x^2+y^2=25[/tex]. Each one of those choices for coordinates has an x and a y. We will fill in the x and y values into our equation to see if the sum of their squares is 25. Going with the first coordinate, (-3, 4), we fill in accordingly: [tex](-3)^2+(4)^2=?[/tex]. -3 squared is 9 and 4 squared is 16. Does 9 + 16 = 25? Yes it does, so a. works for us. Let's try b. now, (1, -2). [tex](1)^2+(-2)^2=?[/tex]. 1 squared is 1 and -2 squared is 4. The addition of those is 5, the length of the radius. But in our standard form for a circle, the radius is a squared value, not a single value. So b. does not work. Last point of [tex]( \sqrt{5}, \sqrt{5}) [/tex]. The square root of 5 squared is 5. Does 5 + 5 = 25? Of course it doesn't. The only point that is on the circle is choice a., (-3, 4).
