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UPSC NDA I 2016 Mathematics Solved Paper

For the next two (2) items that follow.-:

Consider a circle passing through the origin and the points

(a,b)

and

( - b,- a)

[NDA I 2016]

Question : 72 of 120

Marks: +1, -0

Solution:

Suppose;

x^{2}+y^{2}+2gx+2fy+c=0

is the eq. of the circle.

Since; it passes through

(0,0);(a,b)\&(-b,-a)

\therefore C=0

a^{2}+b^{2}+2ga+2fb=0

....(1)

a^{2}+b^{2}-2gb-2fb=0

.....(2)

on solving

g=-f

∴ center

\equiv (-g,-f)

(+f,-f)

∴ from options;

x+y=0

is the line which passes through

(-f,f)

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