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If the straight line xcosalpha+ysinalpha...

If the straight line `xcosalpha+ysinalpha=p` touches the curve `(x^2)/(a^2)-(y^2)/(b^2)=1,` then prove that `a^2cos^2alpha-b^2sin^2alpha=p^2dot`

A

`a^2 sec^2 alpha-b^2 cosec^2 alpha=((a^2+b^2)^2)/(p^2)`

B

`a^2 sec^2 alpha+b^2 cosec^2 alpha=((a^2+b^2)^2)/(p^2)`

C

`a^2 cos^2 alpha-b^2 sin^2 alpha=((a^2+b^2)^2)/(p^2)`

D

`a^2 cos^2 alpha+b^2 sin^2 alpha=((a^2+b^2)^2)/(p^2)`

Text Solution

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The correct Answer is:
A
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