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COMEDK2021MathematicsCircle

What will be the equation of the circle whose centre is (1,2) and which passes through the point (4,6) ?

Options

  1. Ax²+y²-2 x-4 y-20=0
  2. Bx²+y²+2 x+4 y-20=0
  3. Cx²-y²-2 x-4 y+20=0
  4. Dx²-y²+2 x-4 y-20=0

Correct answer

A. x²+y²-2 x-4 y-20=0

Step-by-step solution

The radius r of the circle is the distance between the centre (1, 2) and the point (4, 6) on the circle. r = (4 - 1)² + (6 - 2)² r = 3² + 4² = 9 + 16 = 25 = 5 The equation of a circle with centre (h, k) and radius r is given by (x - h)² + (y - k)² = r² . Substituting (h, k) = (1, 2) and r = 5 : (x - 1)² + (y - 2)² = 5² x² - 2x + 1 + y² - 4y + 4 = 25 x² + y² - 2x - 4y + 5 - 25 = 0 x² + y² - 2x - 4y - 20 = 0 Answer: x²+y²-2 x-4 y-20=0

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