JEE Advanced 2015 Paper 2 Mathematics Q11

Mathematics

Problem

Let

E_1

and

E_2

be two ellipses whose centers 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+(y-1)^2=2

. The straight line

x+y=3

touches the curves

S

E_1

and

E_2

P

Q

and

R

, respectively. Suppose that

PQ=PR=\dfrac{2\sqrt2}{3}

. If

e_1

and

e_2

are the eccentricities of

E_1

and

E_2

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