First slide

Definition of a circle

Question

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

Moderate

A

(4, 7)
B

(7, 4)
C

(9, 4)
D

(4, 9)

Solution

The equations of the sides of the square
$x = 2, x = 6, y = 5$ and $y = 9$ .
Therefore, the coordinates of end points of a diameter are (2, 5) and (6, 9). So, the centre of
square has the coordinates $(\frac{2 + 6}{2}, \frac{5 + 9}{2}) = (4, 7)$
Hence, the coordinates of the centre of the circle are ( 4, 7).

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