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KEAM 2010 Math Paper

Question : 4 of 120

Marks: +1, -0

7 x^{2}-9 y^{2}=63

is equal to

Solution:

Equation of the given conic is

7 x^{2}-9 y^{2}=63

It can be rewritten as

\;\frac{x^{2}}{9}-\;\frac{y^{2}}{7}=1

which is an equation of hyperbola Comparing the above equation with standard equation of hyperbola

\;\frac{x^{2}}{a^{2}}-\;\frac{y^{2}}{b^{2}}=1

, we get

a^{2}=9,\;b^{2}=7\Rightarrow a=3,\;b=\sqrt{7}

Now, Distance between foci is

2ae=2a\sqrt{\frac{a^{2}+b^{2}}{a^{2}}}=2\sqrt{9+7}=2\times 4=8

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