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]}

How do you use the discriminant to classify the conic section 4x^2 + 32x - 10y + 85 = 04x^2 + 32x - 10y + 85 = 0?