Use the discriminant to determine the conic given by #12x^2+6xy+4y^2+58x+20y+190=0# ?

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Answer 1 · 2018-02-21T02:03:15

From the link to the reference we observe that, when #Delta < 0# and #A!=C# and #B!=0# then we have an ellipse.

Given the General Cartesian form of the equation of a conic section:

#Ax^2+Bxy+Cy^2+Dx+Ey + F = 0#

The discriminant, #Delta#, is:

#Delta = B^2 - 4AC#

For the given conic equation:

#12x^2+6xy+4y^2+58x+20y+190=0#

#A = 12#, #B = 6#, and #C = 4#

#Delta = 6^2 - 4(12)(4)#

#Delta = -156#

From the link to the reference we observe that, when #Delta < 0# and #A!=C# and #B!=0# then we have an ellipse.