Equation of the line passing through the points of intersection of the parabola x^2=8y and…

Question

Equation of the line passing through the points of intersection of the parabola $x^2=8y$ and the ellipse $\dfrac{x^2}{3}+y^2=1$ is:

Accepted Answer

Substitute $x^2=8y$ into $\dfrac{x^2}{3}+y^2=1$: $\dfrac{8y}{3}+y^2=1\Rightarrow 3y^2+8y-3=0\Rightarrow y=-3\text{ or }\tfrac13$.

$y=-3$ gives $x^2=-24$, rejected. So $y=\tfrac13$ (a horizontal line through both intersection points):
$$y-\frac13=0\Rightarrow 3y-1=0.$$

Solutions · 1