# An ellipse, with foci at (0,2) and (0, -2) and minor axis of length 4, passes through which of the following points? Option 1) $(\sqrt{2},2)$       Option 2) $(2,\sqrt{2})$ Option 3) $(2,2\sqrt{2})$ Option 4) $(1,2\sqrt{2})$

let   $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$    $(a  is the equation of ellipse , focii $(0,\pm 2)$

Given : 2a = 4 => a = 2

$e^{2}=1-\frac{a^{2}}{b^{2}}=> b^{2}e^{2}=b^{2}-a^{2}$

$4=b^{2}-4$

$8=b^{2}$

$\therefore$ equation of ellipse is

$\frac{x^{2}}{4}+\frac{y^{2}}{8}=1$

=> it passes through $(\sqrt2,2)$

so, option 2 is correct.

Option 1)

$(\sqrt{2},2)$

Option 2)

$(2,\sqrt{2})$

Option 3)

$(2,2\sqrt{2})$

Option 4)

$(1,2\sqrt{2})$

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