The centre of circle inscribed in square formed by the lines x 2 - 8 x + 12 = 0 and y 2 - 14 y + 45 = 0 , is [2003]

Question

The centre of circle inscribed in square formed by the lines $x^{2} - 8 x + 12 = 0$ and $y^{2} - 14 y + 45 = 0$ , is [2003]

Smart Achievers · Accepted Answer

(1)

$x^{2} - 8 x + 12 = 0 \Rightarrow (x - 6) (x - 2) = 0$

$y^{2} - 14 y + 45 = 0 \Rightarrow (y - 5) (y - 9) = 0$

$Hence, sides of square are x = 2, x = 6, y = 5 and y = 9$

Therefore, centre of circle inscribed in square will be

$(\frac{2 + 6}{2}, \frac{5 + 9}{2}) = (4, 7)$

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