SOLUTION: Identify the conic section represented by the equation: y^2 + 2y + 1 = 6x - x^2. Write in standard form and draw the graph.

Question 198055: Identify the conic section represented by the equation: y^2 + 2y + 1 = 6x - x^2. Write in standard form and draw the graph.
Found 2 solutions by vleith, solver91311:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
http://www24.wolframalpha.com/input/?i=y^2+%2B+2y+%2B+1+%3D+6x+-+x^2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First, put it in general form:

You have both an x-squared term and a y-squared term, so you eliminate parabola as the conic type.

The signs on these terms are the same so you eliminate hyperbola.

The coefficients on the high-order terms are equal, so you eliminate ellipse.

This is a circle.

Complete the square on x:

-6 divided by 2 is -3, squared is 9 -- add 9 to both sides:

Complete the square on y:

2 divided by 2 is 1, squared is 1 -- add 1 to both sides:

Factor the two perfect squares:

Center at (3,-1), radius 3. You can draw your own graph.

John

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