What is the equation of a circle with center (2,-1) that passes through the point (3,4)?

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Ace Lowery · Accepted Answer

The circle&#039;s mathematical formula is (x−a)2+(y−b)2=r2 Where (a,b) is the center of the circle and 2 is the radius of the circle.Although we are aware of the circle&#039;s center, we still need to ascertain its radius. The radius is the separation between a circle&#039;s center and any other point on the circle. The circle&#039;s center and a point on the circle are both provided. We must determine the separation between these two points. The formula for calculating the distance between two points is:d=(x2−x1)2+(y2−y1)2The result of substituting the values from the problem&#039;s points is:d=(3−2)2+(4−−1)2d=(3−2)2+(4+1)2d=12+52d=1+25d=26Now, we can enter the values from the problem&#039;s center point and the calculated radius into the formula for the equation of a circle to obtain:(x−2)2+(y−−1)2=(26)2(x−2)2+(y+1)2=26

What is the equation of a circle with center (2,-1) that passes through the point (3,4)?

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