Solving two curves Let two curves be:-
S1: $x^2/9+y^2/4=1$
S2: $y^2=2x$
Now, on solving these two ,by substituting $y^2$ as $2x$ from S2 in S1, I get two values viz. $x=3/2$ and $x=-6$.
But we can clearly see from the graph that the curves intersect at two distinct points in the first and fourth quadrant. So, should not the quadratic equation hence formed in $x$ rather be a whole square viz $(x-3/2)^2$ ?

In general, when you intersect two conics, you can have $4$ intersection points, that's why you see a ghost. 
Imagine if you pinched the parabola and pulled it to the left through the other side of the ellipse. Then you would get $4$ intersections, and the other solution for $x$ would be relevant.
