The equation of the circle would be (x - 1)² + (y - 3)² = 65.
<h3>What is the equation of a circle?</h3>
The equation of a circle with center (h,k) and radius, r in center radius form is given;
(x - h)² + (y - k)² = r²
The coordinates of the center of the circle can be calculated by the formula
((x₁ + x₂)/2, (y₁ + y₂)/2).
The point (x₁,y₁) = (9, 2) and (x₂,y₂) = (-7, 4).
So, ((9 -7)/2, (4 + 2)/2) = (1, 3).
Now, r² = (x₂ - x₁)² + (y₂ - y₁)².
Let (x₁, y₁) = (1, 3) and (x₂, y₂) = (-7, 4).
So, r² = (-7 -1)² + (4 - 3)²
= -8² + 1² = 64 + 1 = 65.
With center (h,k) = (1, 3) and r² = 65, we have
Thus, the equation would be (x - 1)² + (y - 3)² = 65.
Learn more about the equation of circle;
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