The centre of the circle inscribed in a square formed by the lines ` x^(2) - 8x+12 = 0` and ` y^(2) - 14 + 45 = 0` is

Options

A. (4, 7)
B. (7, 4)
C. (9, 4)
D. (4, 9)

Answer

A

Explanation

Given circle is inscribed in square formed by the lines
`x^(2)-8x+12 =0 and y^(2) - 14y + 45 = 0`
`rArr x= 6 and x=2, y =5 and y=9`
which could be plotted as
Where, ABCD clearly forms a square.
`therefore` Centre of inscribed circle
= Point of intersection of diagonals
= Mid point of AC or BD
`=((2+6)/(2)),((5+9)/(2))=(4,7)`
`rArr` Centre of inscribed circle is (4, 7).