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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: |
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Answer» `(SQRT3 +1)/(2)` 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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