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If a variable straight line x cos alpha+...

If a variable straight line `x cos alpha+y sin alpha=p` which is a chord of hyperbola `(x^(2))/(a^(2))=(y^(2))/(b^(2))=1 (b gt a)` subtends a right angle at the centre of the hyperbola, then it always touches a fixed circle whose radius, is (a) `(sqrt(a^2+b^2))/(ab)` (b) `(2ab)/(sqrt(a^2+b^2))` (c) `(ab)/(sqrt(b^2-a^2))` (d) `(sqrt(a^2+b^2))/(2ab)`

Text Solution

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The correct Answer is:
`(ab)/sqrt(b^(2) - a^(2))`
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