Question

*5. identify the x - and y - intercepts of the circle. write as coordinate points!
$x^{2}+x + y^{2}+2y = 0$

Explanation:

Step1: Find x - intercepts

Set \(y = 0\) in the equation \(x^{2}+x + y^{2}+2y=0\).
We get \(x^{2}+x=0\).
Factor out \(x\): \(x(x + 1)=0\).
Solve for \(x\): \(x=0\) or \(x=-1\).
So the x - intercepts are \((0,0)\) and \((-1,0)\).

Step2: Find y - intercepts

Set \(x = 0\) in the equation \(x^{2}+x + y^{2}+2y=0\).
We get \(y^{2}+2y=0\).
Factor out \(y\): \(y(y + 2)=0\).
Solve for \(y\): \(y=0\) or \(y=-2\).
So the y - intercepts are \((0,0)\) and \((0,-2)\).

Answer:

The x - intercepts are \((0,0)\) and \((-1,0)\). The y - intercepts are \((0,0)\) and \((0,-2)\).