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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 9x2y+30=0
Let 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=2AY

A=3X+2Y5

(2,6)=(3h+05,0+2k5)


(2,6)=(3h5,2k5)

2=3h5,6=2k5

h=103,k=15

equation of straight line XY is

y15x0=0151030

y15x=92

9x2y+30=0

Hence the required equation of line is 9x2y+30=0

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