Determine the equation of the circle if its Centre is (8, -6) and which passes
through the point (5, -2).
Answers
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Answer:
Equation of the circle is (x - 8)² + ( y + 6)² = 5² or
x² + y² - 16x + 12y + 75 = 0
Given problem:
Determine the equation of the circle if its Center is (8, -6) and which passes through the point (5, -2).
Step-by-step explanation:
let (x - h)² + (y - k)² = r²_(1) be the required equation of the circle
here (h, k) is center of the circle and r = radius
given that center of the circle = (8, -6)
substitute (8, -6) in (1)
(x - 8)² + (y - (-6))² = r²
(x - 8)² + ( y + 6)² = r² _(2)
(2) passes through (5, -2)
(5 - 8)² + ( -2 + 6)² = r²
(- 3)² + 4² = r²
r² = 9 +16 = 25
r² = 5²
r = 5
the required equation is (x - 8)² + ( y + 6)² = 5²
x² + 64 -16x + y² +36 +12y = 25
x² + y² - 16x + 12y +100 -25 = 0
x² + y² - 16x + 12y + 75 = 0