The endpoints of the diameter of a circle are (6, 5) and (−2, 3). Which equation represents the circle?
1 answer:
Answer:
(x - 2)² + (y - 4)² = 17
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 at the midpoint of the endpoints of the diameter, that is
x = =
= 2 and y =
=
= 4
centre = (2, 4 )
The radius is the distance from the centre to either of the endpoints
Using the distance formula to find r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (- 2, 3)
r =
=
=
= ⇒ r² = 17
Thus the equation of the circle is
(x - 2)² + (y - 4)² = 17
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