(x-8)² + (y-7)² - 17 = 0 is the equation of the circle.
Step-by-step explanation:
(12,8) and (4,6) are the endpoints of the diameter of a circle.
The equation of the circle is given as,
(x-h)² + (y-k)² = r²
where (h,k) is the center and r is the radius of the circle.
We have the endpoints of the diameter, from that we can find the center using the mid - point formula as,
center = ( (1/2)(x₁ + x₂), (1/2)(y₁+y₂))
= ( (1/2)(12+4), (1/2)(8+6))
= ((1/2)(16), (1/2)(14))
= (8,7)
To find the radius we can use the distance formula as, using the center (8,7) and end point (12,8)
r = √((x₂- x₁)² + (y₂-y₁)²)
= √((12- 8)² + (8-7)²)
= √((4² + 1²)) = √(16+ 1) = √17
Squaring on both sides, we will get,
r² = 17
So the equation of the circle can be written as,
(x-8)² + (y-7)² = 17
