Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.

The standard form of the equation for the conic section represented by is:

Step-by-step explanation:

We know that:

is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

Rewriting the equation in the standard form

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by is:

where

vertex (h, k) = (-5, 12)

the correct is answer is a 9-sided polygon!