Circle 1 Question 7

7. 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 $(2003,1 M)$

(a) $(4,7)$

(b) $(7,4)$

(c) $(9,4)$

(d) $(4,9)$

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Answer:

Correct Answer: 7. (a)

Solution:

  1. Given, circle is inscribed in square formed by the lines $x^{2}-8 x+12=0$ and $y^{2}-14 y+45=0$

$\Rightarrow \quad x=6 \quad$ and $x=2, y=5$ and $y=9$

which could be plotted as

where, $A B C D$ clearly forms a square.

$\therefore$ Centre of inscribed circle

$=$ Point of intersection of diagonals

$=$ Mid-point of $A C$ or $B D$

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

$\Rightarrow$ Centre of inscribed circle is $(4,7)$.



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