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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 on the Cartesian plane?
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
Dividing through by 100, completing the square and rearranging gives:
100x² + 100y² - 120x + 100y - 39 = 0
→ x² - (6/5)x + y² + y - 39/100 = 0
→ (x - (6/10))² - (6/10)² +(y + 1/2)² - (1/2)² - 39/100 = 0
→ (x - 3/5)² - 36/100 + (y + 1/2)² - 1/4 - 39/100 = 0
→ (x - 3/5)² + (y + 1/2)² - 1/4 - 75/100 = 0
→ (x - 3/5)² + (y + 1/2)² = 1/4 + 3/4
→ (x - 3/5)² + (y - (-1/2))² = 1 = 1²
→ Circle has centre (3/5, -1/2) = (0.6, -0.5) and radius 1.
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoThe centre is (0.6, -0.5) and the radius is 1.
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