Question

question 9 of 20 which conic section does the equation below describe? ((y + 3)^2=\frac{1}{8}(x - 5)) a. ellipse b. hyperbola c. circle d. parabola

Explanation:

Step1: Recall conic - section equations

The general forms of conic - section equations are used for identification.
The standard form of a parabola with a horizontal axis of symmetry is \((y - k)^2=4p(x - h)\), where \((h,k)\) is the vertex and \(p\) is the distance from the vertex to the focus.

Step2: Rewrite the given equation

The given equation is \((y + 3)^2=\frac{1}{8}(x - 5)\). Here, \(h = 5\), \(k=-3\), and \(4p=\frac{1}{8}\) (so \(p=\frac{1}{32}\)). It is in the form \((y - k)^2 = 4p(x - h)\).

Answer:

D. Parabola