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melodykap

Answered question

2020-11-09

Identify the conic with th e given equation and give its equation in standard form

6 x^{2} - 4 x y + 9 y^{2} - 20 x - 10 y - 5 = 0

odgovoreh

Skilled2020-11-10Added 107 answers

Given

6 x^{2} - 4 x y + 9 y^{2} - 20 x - 10 y - 5 = 0

All degenerate conic sections have equations of the form

A x^{2} + B x y + C y^{2} + D x + E y + F = 0

A x^{2} + B x y + C y^{2} + D x + E y + F = 0

where A,B,C,D,E and F are constants. If

B^{2} - 4 A C

is less than zero, if a conic exists and A = C, it will be a circle If

B^{2} - 4 A C

is less than zero, if a conic exists , it will be ellipse. If

B^{2} - 4 A C

equals zero, if a conic exists, it will be a parabola. If

B^{2} - 4 A C

is greater than zero, if a conic exists, it will be a hyperbola. Here in equation

6 x^{2} - 4 x y + 9 y^{2} - 20 x - 10 y - 5 = 0

B^{2} - 4 A C = 4^{2} - 4 \cdot 6 \cdot 9

= 16 - 216

= - 200 < 0

and

A \neq C

Hence it is an ellipse

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