jee-main 2012 Q69

jee-main · India · 12may Conic sections Chord Properties and Midpoint Problems

If $P_{1}$ and $P_{2}$ are two points on the ellipse $\frac{x^{2}}{4} + y^{2} = 1$ at which the tangents are parallel to the chord joining the points $(0, 1)$ and $(2, 0)$, then the distance between $P_{1}$ and $P_{2}$ is
(1) $2\sqrt{2}$
(2) $\sqrt{5}$
(3) $2\sqrt{3}$
(4) $\sqrt{10}$

If $P_{1}$ and $P_{2}$ are two points on the ellipse $\frac{x^{2}}{4} + y^{2} = 1$ at which the tangents are parallel to the chord joining the points $(0, 1)$ and $(2, 0)$, then the distance between $P_{1}$ and $P_{2}$ is\\
(1) $2\sqrt{2}$\\
(2) $\sqrt{5}$\\
(3) $2\sqrt{3}$\\
(4) $\sqrt{10}$

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