Question

1. which conic section is represented by the equation $x^2 - 8y + y^2 + 11 = 0$?

hyperbola
parabola
ellipse
circle

Explanation:

Step1: Rearrange the given equation

$x^2 + y^2 - 8y = -11$

Step2: Complete the square for $y$-terms

$x^2 + (y^2 - 8y + 16) = -11 + 16$

Step3: Simplify the equation

$x^2 + (y - 4)^2 = 5$

Answer:

Circle