For the conic section the equation

Question

X-2y²=0 which of the following is true ?

a. The graph is an ellipse centered at (0,0)

b. The graph is a hyperbola that passes through (0,0) and (2,1)

c.the length of the minor axis is 2

d. The graph has a focus at (1/8,0)

Answer 1

x - 2y² = 0

x = 2y²

 

This is the equation of a parabola whose vertex is on the origin and which opens to the right.

 

So it can't be a and it can't be b.

 

In addition, a parabola isn't generally said to have a minor axis, though sometimes the term is used to refer to the line tangent to the parabola at the vertex.  When it is used that way, though, the minor axis does not have a finite length.  So c can't be right either.

 

The only choice left is d.

 

That's correct, because the focus of a parabola opening to the right with its vertex on the origin is (1/4a, 0).  In this case, x = 2y², a = 2, so the focus is at (1/8, 0), just as choice d says.