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Kryger [21]
3 years ago
9

The endpoints of a diameter of a circle are located at (5,9) and (11,17) which is an equation of the circle?

Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

(x - 8)² + (y - 13)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre is located at the midpoint of the endpoints of the diameter.

Use the midpoint formula to find the centre

[\frac{x_{1}+x_{2}  }{2}, \frac{y_{1}+y_{2}  }{2} ]

with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)

centre = ( \frac{5+11}{2}, \frac{9+17}{2} ) = (8, 13)

The radius is the distance from the centre to either end of the diameter

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)

r = \sqrt{(5-8)^2+(9-13)^2}

  = \sqrt{(-3)^2+(-4)^2}

  = \sqrt{9+16} = \sqrt{25} = 5 ⇒ r² = 25

Hence

(x - 8)² + (y - 13)² = 25

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