KVPY SX SB Exam 2012 Question Paper

Question : 6 of 120

Marks: +1, -0

Consider the conic

ex^2+πy^2-2e^2x

-2πy+e^3+π^3=πe

. Suppose P is any point on the conic and

S_1, S_2

are the foci of the conic, then the maximum value of

(PS_1 + PS_2)

Solution:

ex^2+πy^2-2e^2x

-2πy+e^3+π^3=πe

e(x^2-2ex+e^2)

+π(y^2-2πy+π^2)=πe

(x-e)^2/π+(y-π)^2/e=1

a^2=π⇒a=√π

(π > e)

PS_1+PS_2=2a

Major axis is || to axis

PS_1+PS_2=2√π

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