Indicate whether the equation represents an ellipse, hyperbola, circle, or parabola. In equations that contain bothth $x ^ { 2 }$ 2 and $y ^ { 2 }$ terms, divide both terms, divide bothsides of the equation by the constant term to put the equation in a more recognizable form.
-$x ^ { 2 } + y ^ { 2 } - 16 x = 80$
A)Ellipse
B)Hyperbola
C)Circle
D)Parabola

Question

Quizplus · Accepted Answer

The equation $x^2 + y^2 - 16x = 80$ can be rewritten in the form of a circle by completing the square for the x-terms. Completing the square involves adding and subtracting $(\frac{16}{2})^2 = 64$ to the equation, leading to $x^2 - 16x + 64 + y^2 = 80 + 64$, which simplifies to $(x-8)^2 + y^2 = 144$. This is the standard form of a circle's equation, $(x-h)^2 + (y-k)^2 = r^2$, indicating that the original equation represents a circle.

Indicate Whether the Equation Represents an Ellipse, Hyperbola, Circle, or Parabola