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

ellipse

hyperbola

circle

parabola

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)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.