Question

identify the type of conic section given by the following equation:

(x^2 - 8x + 8y + 56 = 0)

• parabola
• ellipse
• hyperbola
• degenerate conic

Explanation:

Step1: Identify the given equation

$$x^2 - 8x + 8y + 56 = 0$$

Step2: Analyze the squared terms

Only one variable, \(x\), is squared in the equation.

Step3: Determine the conic type

A conic section with only one squared variable is a parabola.

Answer:

Parabola