Question

A square is formed by the two points of straight lines x² – 8x + 12 = 0 and y² – 14y + 45 = 0. A circle is inscribed in it. The centre of the circle is

(a) (6, 5)

(B) (5, 6)

(c) (7, 4)

(d) (4, 7)

Answer 1

The correct option (d) (4, 7)  

Explanation:

x² – 8x + 12 = 0

⇒   (x – 6)(x – 2) = 0 

also   y² – 14y + 45 = 0

⇒  (y – 5)(y – 9) = 0

∴ sides of square are

x = 2, x = 6, y = 5 and y = 9.

∴ centre of circle inscribed in the square will be given by

[{(2 + 6)/2}, {(5 + 9)/2}] = (4, 7)

∴ option d is centre of circle.