Question

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be

Answer 1

The equation of the circle would be (x - 1)² + (y - 3)² = 65.

What is the equation of a circle?

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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