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COMEDK2021MathematicsCircle

Find the centre and radius of the circle given by the equation 2 x²+2 y²+3 x+4 y+ 9 8 =0 .

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

A. 1

Step-by-step solution

The given equation of the circle is 2x² + 2y² + 3x + 4y + 9 8 = 0 . Dividing the entire equation by 2 , we get x² + y² + 3 2 x + 2y + 9 16 = 0 . Comparing this with the standard form x² + y² + 2gx + 2fy + c = 0 , we identify 2g = 3 2 g = 3 4 and 2f = 2 f = 1 . The centre of the circle is (-g, -f) = (- 3 4 , -1 ) . The radius r is given by g² + f² - c = ( 3 4 )² + (1)² - 9 16 = 9 16 + 1 - 9 16 = 1 = 1 . Answer: 1

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