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Question

If the curves x2a2+y2b2=1 and x2α2+y2β2=1 cut each other orthogonally,


A
a2+b2=α2+β2
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B

a2b2=α2β2

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C

a2b2=α2+β2

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D
a2+b2=α2β2
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Solution

The correct option is A a2+b2=α2+β2

Slope of I=b2xa2y=m1 (say),
And slope of II =β2α2y=m2(say)m1m2=1b2β2x2=a2α2y2
and x2a2+y2b21=0
x2α2y2β21=0x2(1a21α2)=y2(1b21β2)
From Eqs. (i) and (ii)
1a21α2b2β2=(1b21β2)a2α2α2+β2=a2+b2
note: remember it as formula


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