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Bezzdna [24]
3 years ago
12

What conic section does the equation x2 + y2 – 4y – 1 = 0 represent?

Mathematics
1 answer:
irakobra [83]3 years ago
5 0
The conic section that the above equation represents is a CIRCLE.

Use completing the square for y and put the equation in standard form: 
<span>x</span>²<span>+ y</span>²<span> - 4y + [(-4)/2]</span>²<span> - 1 = 0 + [(-4)/2]</span>²
<span>x</span>²<span> + y</span>²<span> - 4y + (-2)</span>²<span> - 1 = 0 + (-2)</span>²
<span>x</span>²<span> + y</span>²<span> - 4y + 4 - 1 = 4 </span>
<span>x</span>²<span> + (y - 2)</span>²<span> - 1 = 4 </span>
<span>x</span>²<span> + (y - 2)</span>²<span> = 4 + 1
</span>x² + (y -2)² = 5

The radius of the circle is the square root of 5. Its center is found at (0,2)

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