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

SSC CGL Model Paper 15

Question : 69 of 100

Marks: +1, -0

2x^2 + 2y^2 = 4a

, then find the value of

{2a}/{x^2-a}+{2a}/{y^2-a}

Solution:

2x^2 + 2y^2 = 4a

...(1)

x^2+y^2=2a

....(2)
Now,

{2a}/{x^2-a}+{2a}/{y^2-a}

{2a}/{(2a-y^2)-a}+{2a}/{(2a-x^2)-a}

[from (2)]

{2a}/{a-y^2}+{2a}/{a-x^2}

={2a^2-2ax^2+2a^2-2ay^2}/{(a-y^2)(a-x^2)}

={4a^2- a(2x^2+2y^2)}/{(a-y^2)(a-x^2)}=0

[from (1)]

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