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NDA Math Circle

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 : 22 of 26

Marks: +1, -0

Solution:

The two intercepts are :

-2g

-2f

∴ from eq (1) & (2) we get;

g=\;\;\frac{-1}{2}\left(\;\;\frac{a^{2}+b^{2}}{a-b}\right)\&f=\;\;\frac{1}{2}\left(\;\;\frac{a^{2}+b^{2}}{a-b}\right)

is sum of squares of intercepts

=\left(\;\;\frac{a^{2}+b^{2}}{a-b}\right)^{2}+\left(\;\;\frac{a^{2}+b^{2}}{a-b}\right)^{2}

=2\left[\;\;\frac{a^{2}+b^{2}}{a-b}\right]^{2}

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