melodykap

2020-11-09

Identify the conic with th e given equation and give its equation in standard form $6{x}^{2}-4xy+9{y}^{2}-20x-10y-5=0$

odgovoreh

Skilled2020-11-10Added 107 answers

Given $6{x}^{2}-4xy+9{y}^{2}-20x-10y-5=0$
All degenerate conic sections have equations of the form $A{x}^{2}+Bxy+C{y}^{2}+Dx+Ey+F=0$ .

$A{x}^{2}+Bxy+C{y}^{2}+Dx+Ey+F=0$ where A,B,C,D,E and F are constants.
If ${B}^{2}-4AC$ is less than zero, if a conic exists and A = C, it will be a circle
If ${B}^{2}-4AC$ is less than zero, if a conic exists , it will be ellipse.
If ${B}^{2}-4AC$ equals zero, if a conic exists, it will be a parabola.
If ${B}^{2}-4AC$ is greater than zero, if a conic exists, it will be a hyperbola.
Here in equation $6{x}^{2}-4xy+9{y}^{2}-20x-10y-5=0$ ,
${B}^{2}-4AC={4}^{2}-4\cdot 6\cdot 9$

$=16-216$

$=-200<0$
and $A\ne C$
Hence it is an ellipse

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