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P is a point (a , b) in the first quadra...

`P` is a point `(a , b)` in the first quadrant. If the two circles which pass through `P` and touch both the coordinates axes cut at right angles, then `a^2-6a b+b^2=0` `a^2+2a b-b^2=0` `a^2-4a b+b^2=0` `a^2-8a b+b^2=0`

A

`alpha^(2) + beta^(2) = 4 alpha beta`

B

`(alpha + beta)^(2) = 4 alpha beta`

C

`alpha^(2) +beta^(2) = alpha beta`

D

`alpha^(2) +beta^(2) = 2 alpha beta`

Text Solution

Verified by Experts

The correct Answer is:
A
For orthogonal of two circle `2(r_(1)-r_(2))^(2) = r_(1)^(2) +r_(2)^(2)`
`rArr (r_(1)+r_(2))^(2) = 6r_(1)r_(2)`
`rArr 4(alpha + beta)^(2) = 6 (alpha^(2)+beta^(2))`
`rArr alpha^(2) + beta^(2) = 4 alpha beta`
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