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High School
Geometry
High school geometry
Conic sections

chillywilly12a

Answered question

2021-02-25

Identify the graph of the given nondegenerate conic sections:

3 x^{2} + 2 y^{2} + 12 x - 4 y + 2 = 0

Answer & Explanation

insonsipthinye

Skilled2021-02-26Added 83 answers

Step 1 A nondegenerate conic section of the form, $A x^{2} + B y^{2} + C x + D y + E = 0$ Where A and B both are not zero.

1) A circle if $A = B$

2) A parabola if $A B = 0$

3) An ellipse if A is not equal to $B a n d A B > 0$

4) A hyperbola if $A B < 0$

Step 2 Given that, $3 x^{2} + 2 y^{2} + 12 x - 4 y + 2 = 0$ Here $A = 3 a n d B = 2$ So A and B are not equal and $A B = (3) (2) = 6 > 0$ Hence the graph of the equation is ellipse.

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