Question

The number of ordered pairs of integers (x,y) satisfying the equation
$x^2+6x+y^2=4$ is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is D 8

Given,

$x^2+6x+y^2=4$

$\Rightarrow x^2+6x+9+y^2=4+9$

$\Rightarrow x^2+3^2+2\left(3x\right)+y^{=}13$

$\Rightarrow (x+3{)}^2+y^2=13$

sum of two squares is $13$

$\therefore$ when $(x+3{)}^2=9,x=0,-6$ and $y^2=2,-2$ $\Rightarrow 4$ ordered pairs.

$\therefore$ when $(x+3{)}^2=4,x=-1,-5$ and $y^2=3,-3$ $\Rightarrow 4$ ordered pairs.

A total of $8$ pairs.