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

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify the conic section represented by the equation: y^2 + 2y + 1 = 6x - x^2. Write in standard form and draw the graph.      Log On


   

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) About Me  (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) About Me  (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