If \Bigg(x/a\Bigg)^2+\Bigg(y/b\Bigg)^2=1, (a\gtb) and x^2-y^2=c^2 cut at righ...

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Question Id : 11141 | Context :NIMCET 2022

${\Bigg{(}\frac{x}{a}\Bigg{)}}^2+{\Bigg{(}\frac{y}{b}\Bigg{)}}^2=1$ ,

$(a{\gt}b)$ and

${x}^2-{y}^2={c}^2$ cut at right angles, then

🎥 Video solution / Text Solution of this question is given below:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$\frac{x^2}{c^2}+\frac{y^2}{d^2}=1$ are orthogonal.

Then

$a^2-b^2=c^2-d^2$

Similarly

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$x^2-y^2=c^2$ are orthogonal.

It means

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and

$\frac{x^2}{c^2}+\frac{y^2}{-c^2}=1$ are orthogonal

Then

$a^2-b^2=c^2-(-c^2)$

$a^2-b^2=2c^2$

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