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What is the centre and radius of the circle whose equation is 100x2 plus 100y2 -120x plus 100y -39 equals 0?
Wiki User
∙ 6y ago
A circle with centre (X, Y) and radius r has an equation of the form:
(x - X)² + (y - Y)² = r²
Equation of circle:
100x² + 100y² - 120x + 100y - 39 = 0
Divide all terms by 100:
x² + y² - 1.2x + y - 0.39 = 0
Rearrange bringing x terms and y terms together:
x² - 1.2x + y² + y - 0.39 = 0
Completing the squares:
(x - 1.2/2)² - (1.2/2)² + (y + 1/2)² - (1/2)² - 0.39 = 0
Collect the numbers together on the right hand side:
(x - 0.6)² - 0.6² + (y + 0.5)² - 0.5² - 0.39 = 0
(x - 0.6)² + (y + 0.5)² = 0.36 + 0.25 + 0.39
(x - 0.6)² + (y + 0.5)² = 1 = 1²
Centre of circle: (0.6, -0.5)
Radius of circle: 1
Wiki User
∙ 6y ago
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