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Phantasy [73]
3 years ago
8

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

Mathematics
1 answer:
marusya05 [52]3 years ago
3 0

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.

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