The type of conic sections for the nondegenerate equations given below.a) 8x^{2} - 2y^{2} - 3x + 2y - 6=0b) -6y^{2} + 4x - 12y - 24=0c) -9x^{2} - 4y^{2} - 18x + 12y=0

Lennie Carroll

Lennie Carroll

Answered question

2020-11-08

The type of conic sections for the nondegenerate equations given below.

a) 8x2  2y2  3x + 2y  6=0 

b) 6y2 + 4x  12y  24=0

c) 9x2  4y2  18x + 12y=0

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2020-11-09Added 97 answers

Step 1

a) Consider the equation 8x2  2y2  3x + 2y  6=0 It is known that the equation of conic section is in the form Ax2 + Cy2 + Dx + Ey + F=0 In the given equation, the coefficient of x2 and y2 are A=8 and C= 2, respectively, which means AC= 16, that is, AC < 0. Therefore, this is the equation of a hyperbola. Hence, the conic section of the given equation is a hyperbola.

Step 2

b) Consider the equation 6y2 + 4x  12y  24=0. It is known that the equation of conic section is in the form Ax2 + Cy2 + Dx + Ey + F=0. Here, the given equation does not have the term of x2, which means A=0, that is, AC=0. Therefore, this is the equation of parabola. Hence, the conic section of the given equation is a parabola. Step 3 c) Consider the equation 9x2  4y2  18x + 12y=0. It is known that the equation of conic section is in the form Ax2 + Cy2 + Dx + Ey + F=0. In the given equation, the coefficient of x2 and y2 are A= 9 and C= 4, respectively, which means AC=36, that is, AC > 0. Therefore, this is the equation of an ellipse. Hence, the conic section of the given equation is an ellipse.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?