1.

If a circle of radius 3 units is touching the lines sqrt3 y^2 - 4xy +sqrt3 x^2= 0 in the first quadrant then length of chord of contact to this circle is:

Answer»

`(SQRT3 +1)/(2)`
`(sqrt3+1)/(sqrt2)`
`3((sqrt3+1)/(sqrt2))`
`(3(sqrt3+1))/(2)`

SOLUTION :
Given equation of lines `sqrt3 y^2 - 4xy +sqrt3 x^2 = 0`
`sqrt3 y^2 - 3xy - xy + sqrt3 x^2 = 0`
`rArr (sqrt3 y- x)(y-sqrt3 x) = 0 rArr y = (x)/(sqrt3) , y = sqrt3x`
`angle APO = 75^@`
LENGTH of chord of contact AB
` = 2.3 sin 75^@ = 6(sin 45^@ cos 30^@ + sin 30^@ cos 45^@)`
`6((1)/(sqrt2) .(sqrt3)/(2) + 1/2 . (1)/(sqrt2)) = (6(sqrt3+1))/(2sqrt2) = (3(sqrt3 + 1))/(sqrt2)`


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