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AIEEE 2003

JEE Main 2003 Mathematics question on Circles

The centre of circle inscribed in square formed by the lines x2−8x+12=0x^2 - 8x + 12 = 0 and y2−14y+45=0y^2 - 14y + 45 = 0, is
  1. A.
    (4, 7)
  2. B.
    (7, 4)
  3. C.
    (9, 4)
  4. D.
    (4, 9)
Show answer and solution

Correct option: A

Solution

The lines x²-8x+12=0 factor as (x-2)(x-6)=0, giving x=2 and x=6. The lines y²-14y+45=0 factor as (y-5)(y-9)=0, giving y=5 and y=9. These four lines form a square, and the inscribed circle's centre is simply the midpoint of the square: x = (2+6)/2 = 4, y = (5+9)/2 = 7, giving centre (4, 7).

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