The points (3,-2) and (-2,3) lie on a circle whose center is on the x-axis. What is the radius of the circle?
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+9488 Let the center of the circle be (h, 0)
distance between (h, 0) and (3, -2) = distance between (h, 0) and (-2, 3)
√(−2−0)2+(3−h)2 = √(−2−h)2+(3−0)2 (−2−0)2+(3−h)2=(−2−h)2+(3−0)2 (−2−0)2−(3−0)2=(−2−h)2−(3−h)2
Notice here that if h = 0 both sides of the equation are identical.
If you want to, you can expand both sides to also find that h = 0.
So the center of the circle is (0, 0)
And the radius = √(−2−0)2+(3−0)2 = √4+9 = √13
Here's a graph: https://www.desmos.com/calculator/najnuubd4e
+9488 Let the center of the circle be (h, 0)
distance between (h, 0) and (3, -2) = distance between (h, 0) and (-2, 3)
√(−2−0)2+(3−h)2 = √(−2−h)2+(3−0)2 (−2−0)2+(3−h)2=(−2−h)2+(3−0)2 (−2−0)2−(3−0)2=(−2−h)2−(3−h)2
Notice here that if h = 0 both sides of the equation are identical.
If you want to, you can expand both sides to also find that h = 0.
So the center of the circle is (0, 0)
And the radius = √(−2−0)2+(3−0)2 = √4+9 = √13
Here's a graph: https://www.desmos.com/calculator/najnuubd4e
