Answer:
The line [tex]y=-6[/tex] never intersects with the circle [tex]x^{2} +y^{2} =6[/tex]
Step-by-step explanation:
The equation of a circle with center [tex](h,k)[/tex] and radius of [tex]r[/tex] units is given by:
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
So, for the circle:
[tex]x^{2} +y^{2} =6[/tex]
[tex]h=0\\k=0\\r=\sqrt{6}\approx 2.54[/tex]
Which is a circle centered at the origin and radius of 2.45.
The line [tex]y=-6[/tex] is a horizontal line with a constant value of -6. Hence, the line never intersect the circle.
I attached you the graphs.
