Question 4

If $$2x^2+2y^2=4a$$, then find the value of $$\frac{2a}{x^2-a}+\frac{2a}{y^2-a}$$

Solution

Given : $$2x^2+2y^2=4a$$

=> $$x^2+y^2=2a$$ -----------(i)

To find : $$\frac{2a}{x^2-a}+\frac{2a}{y^2-a}$$

= $$2a(\frac{1}{x^2-a}+\frac{1}{y^2-a})$$

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

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

Substituting value from equation (i), we get :

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

= $$2a\times0=0$$

=> Ans - (A)

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