Question

How many times does the line y = -6 intersect with the circle x + y = 6

Answer 1

Answer:

The line $y=-6$ never intersects with the circle $x^{2} +y^{2} =6$

Step-by-step explanation:

The equation of a circle with center $(h,k)$ and radius of $r$ units is given by:

$(x-h)^{2} +(y-k)^{2} =r^{2}$

So, for the circle:

$x^{2} +y^{2} =6$

$h=0\\k=0\\r=\sqrt{6}\approx 2.54$

Which is a circle centered at the origin and radius of 2.45.

The line $y=-6$ is a horizontal line with a constant value of -6. Hence, the line never intersect the circle.

I attached you the graphs.