How do you use the discriminant to classify the conic section #4x^2 + 32x - 10y + 85 = 0#?

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Answer 1 · 2016-11-14T14:12:58

The equation represents a parabola.

Comparing this equation to

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

#4x^2+32x-10y+85=0#

#A=4#

#B=0#

#C=0#

#D=32#

#E=-10#

#F=85#

We calculate the discriminant

#Delta=B^2-4AC=0-4*4*0=0#

As #Delta=0#, this equation represents a parabola.

If #Delta<0#, it's an ellipse

If #Delta>0#, it's a hyperbola

graph{4x^2+32x-10y+85=0 [-19.6, 20.93, -3.2, 17.08]}