Find the equation of the circle with center at (-3, 1) and through the point (2, 13).
Find the equation of the circle with center at (3, 2) and through the point (5, 4).
Find the equation of the circle with center at (3, 2) and through the point (5, 4).
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Find radius using distance formula
d= r=√[(-3 -2)²+(1 - 13)²] = √ [(-5)² + (-12)²] = √(25 + 144) = √169 = 13
Center (-3, 1) radius 13 : (x - h)² + (y - k)² = r² with center (h, k) and radius r
(x- -3)² + (y - 1)² = 13²
(x + 3)² + (y - 1)² = 169
You try #2 on your own.
d= r=√[(-3 -2)²+(1 - 13)²] = √ [(-5)² + (-12)²] = √(25 + 144) = √169 = 13
Center (-3, 1) radius 13 : (x - h)² + (y - k)² = r² with center (h, k) and radius r
(x- -3)² + (y - 1)² = 13²
(x + 3)² + (y - 1)² = 169
You try #2 on your own.
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I'm sure you know the formula for making the equation of the circle if you have the center and the radius or diameter. You can find the radius of each of these circles by finding the length of the line from the center to the point in the circle given. Remember the Pythagorean theorem giving the hypotenuse C or a right triangle with legs A and B: A^2 + B^2 = C^2. Given two points (X1, Y1) and (X2, Y2), the distance of the line from one to the other is SQRT((X1 - X2) + (Y1 - Y2)) Make sure you subtract the X and Y coordinates in the same order as each other. SQRT stands for Square Root.