Is a Parabola an Ellipse?

Q. An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latus rectum of parabola are the vertices of a square. The eccentricity of the ellipse is

Q. If the vertices of the ellipse $9x^2+25y^2-18x+100y-116=0$ are the extremities of latus rectum of a parabola whose vertex is $(x_1,y_1)$ where $y_1>-2,$ then

Q. A parabola is drawn with focus at one of the foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ (where $a>b$) and directrix passing through the other focus and perpendicular to the major axes of the ellipse. If latus rectum of the ellipse and the parabola are same, then the eccentricity of the ellipse is

Q. Statement 1: An equation of a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$ is $y=2x+2\sqrt{3}$.
Statement 2: If the line $y=mx+\frac{4\sqrt{3}}{m},(m\ne 0)$ is a common tangent to the parabola $y^2=16\sqrt{3}x$ and the ellipse $2x^2+y^2=4$, then $m$ satisfies $m^4+2m^2=24$

Q. If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b>a)$ and the parabola $y^2=4ax$ cut at right angles, then eccentricity of the ellipse is: