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If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be
found First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is
the distance from the center to endpoint of the diameter. Finally use the center-radius form to find the equation.
Find the center-radius form for the circle having the endpoints
(9,2) and (-7,4) of a dmiameter.
Type an equation.).

Sagot :

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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