For the conic section with the equation

Question

X² + 4x +8y -20=0 which of the following is true 

a. The graph is a parabola with its vertex at (-2,3)

b.the gragh is an ellipse centered at (-2,3)

c. The graph is a hyperbola that passes through (-2,3) and (3,0)

d.the graph has an asymptote at y=-7/3x+10

Answer 1

x² + 4x +8y - 20 = 0

 

You can see that there is a square term for x, but not for y.  A curve that has a square term for one variable but not the other is a parabola.

 

That means that b and c cannot be correct.

 

Also, parabolas do not have asymptotes, so d can't be correct either.

 

The only answer left is a.