Question

find the center and radius of the circle x2+y2-8x-10y-12=0.

Answer 1

Given

• Equation of the circle is x² + y² - 8x - 10y - 12 = 0.

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To find

• Centre and radius of the circle.

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Solution

• We have an equation of a circle. Solving this equation by completing the square.

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→ x² - 8x + y² - 10y - 12 = 0

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→ x² - 8x + (4)² - (4)² + y² - 10y + (5)² - (5)² - 12 = 0

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→ (x - 4)² + (y - 5)² - 16 - 25 - 12 = 0

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→ (x - 4)² + (y - 5)² - 53 = 0

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→ (x - 4)² + (y - 5)² = 53

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→ (x - 4)² + (y - 5)² = (√53)²⠀⠀.... [1]

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Standard equation of a circle is

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⟹ (x - h)² + (y - k)² = r²⠀⠀.... [2]

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Comparing [1] and [2], we get

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→ Center of circle = (h,k) = (4,5)

→ Radius = r = √53

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Hence,

• Centre of the circle is (4,5) and radius of the circle is √53.