iran-konkur 2021 Q146

iran-konkur · Other · konkur-riazi_1400_specialized Conic sections Equation Determination from Geometric Conditions
146. The parabola $6 = 6y - 12y - (x-1)^2$ has vertex $F$ and focus $F'$. An ellipse has foci $F$ and $F'$ and eccentricity $0.6$. What is the distance from the center of the ellipse to the origin?
(1) $1$ (2) $\sqrt{2}$ (3) $\sqrt{3}$ (4) $2$
\textbf{146.} The parabola $6 = 6y - 12y - (x-1)^2$ has vertex $F$ and focus $F'$. An ellipse has foci $F$ and $F'$ and eccentricity $0.6$. What is the distance from the center of the ellipse to the origin?

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(1) $1$ \hfill (2) $\sqrt{2}$ \hfill (3) $\sqrt{3}$ \hfill (4) $2$

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