SATHEE: Circle 1 Question 7

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) $(7, 4)$

(d) $(4, 9)$

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Answer:

Correct Answer: 7. (a)

Solution:

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

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

which could be plotted as

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

$∴$ 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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Circle 1 Question 7

7. The centre of circle inscribed in square formed by the lines x2−8x+12=0 and y2−14y+45=0, is (2003,1M)

Answer:

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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 $(2003, 1 M)$