Which of the following points lies on the circle whose center is at the origin and whose radius is 5? a) (-3, 4) b) (1, -2) c)

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   .  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:  .  -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).   .  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  .  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).

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X=-4 the correct answer