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Definition of circle

The centre of...

Question

The centre of circle inscribed in a square formed by lines $x^{2} - 8 x + 12 = 0$ and $y^{2} - 14 y + 45 = 0$ is?

A

(4, 7)

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B

(7, 4)

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C

(9, 4)

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D

(4, 9)

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Solution

The correct option is A $(4, 7)$
$x^{2} - 8 x + 12 = 0 ⟹ x = 6, x = 2$
$y^{2} - 14 y + 45 = 0 ⟹ y = 5, y = 9$
Center of circle is given by $(\frac{6 + 2}{2}, \frac{5 + 9}{2}) = (4, 7)$

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