SOLUTION: Find the conic section represented by the equation x^2 - 4x + y^2 = y^2 + 8x + 20

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Question 1209660: Find the conic section represented by the equation

x^2 - 4x + y^2 = y^2 + 8x + 20
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
1. **Simplify the equation:**
Subtract y² from both sides:
x² - 4x = 8x + 20
2. **Rearrange the terms:**
x² - 12x - 20 = 0
3. **Analyze the equation:**
The equation is in the form of a quadratic equation in x, and there is no y term. This indicates that the equation represents a parabola.
Therefore, the conic section represented by the given equation is a **parabola**.

Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the conic section represented by the equation

x^2 - 4x + y^2 = y^2 + 8x + 20
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Reduce to the standard form

x^2 - 12x - 20 = 0.

This equation does not represents any conic section
(neither circle, nor ellipse, nor parabola, and nor hyperbola).


ANSWER. This equation does not represent any conic section.

The answer in the post by @CPhill is INCORRECT.