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

Nov 14, 2016

The equation represents a parabola.

#### Explanation:

Comparing this equation to

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

$4 {x}^{2} + 32 x - 10 y + 85 = 0$

$A = 4$

$B = 0$

$C = 0$

$D = 32$

$E = - 10$

$F = 85$

We calculate the discriminant

$\Delta = {B}^{2} - 4 A C = 0 - 4 \cdot 4 \cdot 0 = 0$

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]}