Let `P(alpha,beta)` be a point in the first quadrant. Circles are drawn through P touching the coordinate axes.
Equation of common chord of two circles is

Options

A. A. `x +y = alpha - beta`
B. B. `x +y = 2 sqrt(alpha beta)`
C. C. `x +y = alpha +beta`
D. D. `alpha^(2) -beta^(2) = 4 alpha beta`

Answer

C

Explanation

`S_(1) = x^(2) +y^(2) - 2r_(i)(x+y) +r_(i)^(2) =0`, where `i =1,2`
Thus, equation of common chord.
`2(r_(2)-r_(1)) (r+y) +r_(1)^(2) -r_(2)^(2) =0`
`rArr 2(x+y) = (r_(1)+r_(2)) = 2 (alpha + beta)`
`rArr x +y = alpha + beta`.