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Ellipse question

2015 · Shift 2 · Q29

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2015 · Shift 2 · Q29

Ellipse question

2015 · Shift 2 · Q29

JEE AdvancedMathematicsEllipseMultiple correct+4 / −1

Let

{E_1}

and

{E_2}

be two ellipses whose centres are at the origin. The major axes of

{E_1}

and

{E_2}

lie along the

x

-axis and the

y

-axis, respectively. Let

S

be the circle

{x^2} + {\left( {y - 1} \right)^2} = 2

. The straight line

x+y=3

touches the curves

S

,

{E_1}

and

{E_2}

at

P, Q

and

R

respectively. Suppose that

PQ = PR = {{2\sqrt 2 } \over 3}

. If

{e_1}

and

{e_2}

are the eccentricities of

{E_1}

and

{E_2}

, respectively, then the correct expression(s) is (are)

A
$\mathop e olimits_1^2 + \mathop e olimits_2^2 = {{43} \over {40}}$
B
${e_1}{e_2} = {{\sqrt 7 } \over {2\sqrt {10} }}$
C
$\left| {\mathop e olimits_1^2 + \mathop e olimits_2^2 } \right| = {5 \over 8}$
D
${e_1}{e_2} = {{\sqrt 3 } \over 4}$

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