Question 129

If $$\frac{x}{y}\ $$=$$\ \frac{a+2}{a-2}$$, then the value of $$\ \frac{x^{2}-y^{2}}{x^{2}+y^{2}}\ $$is:

Solution

Given : $$\frac{x}{y}= \frac{a+2}{a-2}$$

Squaring both sides, we get :

=> $$\frac{x^2}{y^2}= \frac{(a+2)^2}{(a-2)^2}$$

Using componendo and dividendo,

=> $$\frac{x^2-y^2}{x^2+y^2}=\frac{(a+2)^2-(a-2)^2}{(a+2)^2+(a-2)^2}$$

= $$\frac{(a^2+4a+4)-(a^2-4a+4)}{(a^2+4a+4)+(a^2-4a+4)}$$

= $$\frac{8a}{2a^2+8}$$

= $$\frac{4a}{a^2+4}$$

=> Ans - (B)

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