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UPSC NDA II 2014 Mathematics Paper

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For the next two (02) items that follow:

Consider the circles

x^2+y^2+2ax+c=0

and

x^2+y^2+2by+c=0

[NDA II 2014]

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Question : 49 of 120

Marks: +1, -0

What is the distance between the centres of the two circles ?

$\sqrt{a^2+b^2}$
$a^2+b^2$
$a+b$
$2(a+b)$

Solution:

x^2+y^2+2ax+c=0

\Rightarrow x^2+2ax+a^2+y^2=a^2-c

\Rightarrow (x+a)^2+y^2=a^2-c

center

\equiv (-a,0)

Similarly,for the second circle

x^2+(y+b)^2=b^2-c

center

\equiv (0,-b)

Distance between the circles

=\sqrt{(-a-0)^2+(0-(-b))^2}=\sqrt{a^2+b^2}

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