Question

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

ellipse

hyperbola

circle

parabola

Answer 1

The conic section that the above equation represents is a CIRCLE.

Use completing the square for y and put the equation in standard form:
x²+ y² - 4y + [(-4)/2]² - 1 = 0 + [(-4)/2]²
x² + y² - 4y + (-2)² - 1 = 0 + (-2)²
x² + y² - 4y + 4 - 1 = 4
x² + (y - 2)² - 1 = 4
x² + (y - 2)² = 4 + 1
x² + (y -2)² = 5

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