`x^2-x y+y^2-4x-4y+16=0` represents a. a point b. a circle c. a pair of straight line d. none of these

Options

A. a point
B. a circle
C. a pair of straight lines
D. none of these

Answer

1

Explanation

Given equation is
`x^(2) - (y + 4)x + y^(2) - 4y + 16 = 0`
Since x is real, we have
`D ge 0`
`rArr (y + 4)^(2) - 4(y^(2) - 4y + 16) ge 0`
or `-3y^(2) + 24y - 48 ge 0`
or `y^(2) - 8y + 16 le 0`
or `(y - 4)^(2) le 0`
or y - 4 = 0
or y = 4
Since the equation is symmetric in x and y, we have x = 4 only.