Question

# The equation straight line is such that it passes through point (−2,6) and the portion of the line intercepted between the axes is divided at this point in the ratio 3:2 is :

A
2x9y=10
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B
9x2y+30=0
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C
9x2y=10
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D
x+2y=10
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Solution

## The correct option is C 9x−2y+30=0Let the required line intercept the y-axis at Y(0,k) and the x-axis at X(h,0).Now, it is given that A divides the line XY in ratio 1:2 internally.∴3AX=2AYA=3X+2Y5⟹(−2,6)=(3h+05,0+2k5)⟹(−2,6)=(3h5,2k5)⟹−2=3h5,6=2k5h=−103,k=15∴ equation of straight line XY is y−15x−0=0−15−103−0⟹y−15x=929x−2y+30=0Hence the required equation of line is 9x−2y+30=0​

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