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COMEDK2021MathematicsCircle

What will be the equation of circle whose centre is (1,2) and touches X - axis?

Options

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

Correct answer

A. x²+y²-2 x-4 y+1=0

Step-by-step solution

The centre of the circle is given as (h, k) = (1, 2) . Since the circle touches the X-axis, the radius r of the circle is equal to the absolute value of the y-coordinate of the centre. Thus, r = |k| = |2| = 2 . The standard equation of a circle with centre (h, k) and radius r is (x - h)² + (y - k)² = r² . Substituting the values h = 1 , k = 2 , and r = 2 into the equation: (x - 1)² + (y - 2)² = 2² Expanding the terms: (x² - 2x + 1) + (y² - 4y + 4) = 4 Simplifying the equation: x² + y² - 2x - 4y + 5 = 4 x² + y² - 2x

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