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Classify the coincs.


Classify the coincs.
1. x2 -8x + y = -2
2. x2 + y2 - 6x - 10y = 2
3. x2 + 10x - 8y = -73
4. 9x2 - 4y2 + 54x + 8y + 41 = 0
5. 9x2 + 4y2 - 72x - 32y = -172
6. 4x2 + 25y2 + 16x + 50y - 59 = 0
7. x2 + 2x +y2 + 6y = 15

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1 Answer

In order to classify conic sections, I recommend that you get all of the variables on the same side of the equal sign (these are already set up in this form), then go through the following flow chart:

1)  Are both x and y squared?
If no, it is is a parabola.
If yes, continue to question 2.

2)  Are the coefficients of x2 and y2 both positive?
If no, it is a hyperbola.
If yes, continue to question 3.

3)  Are the coefficients of x2 and y2 the same?
If no, it is an ellipse.
If yes, it is a circle.

Using the flowchart from above, we can look at each the conic sections that you listed.

1.  1)No.  It is a parabola

2.  1)Yes.  2)Yes.  3)Yes.  It is a circle

3.  1)No.  It is a parabola

4.  1)Yes.  2)No.  It is a hyperbola

5.  1)Yes.  2)Yes.  3)No.  It is an ellipse

6.  1)Yes.  2)Yes.  3)No.  It is an ellipse

7.  1)Yes.  2)Yes  3)Yes.  It iscircle