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Question

The equation of the straight line passing through the origin and the middle point of the portion of the line ax + by + c = 0 between the axes, is



A

ax + by = 0

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B

ax – by = 0

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C

bx + ay = 0

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D

bx – ay = 0

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Solution

The correct option is B

ax – by = 0


The equation of the given line is ax + by + c = 0

ax+by=cxca+yc/b=1                 .......(1)

Let the line (1) cuts x-axis and y-axis at the points A and B respectively, then

A(ca,0)and B(0,cb)

The coordinates of the middle point C of AB are

(ca2,0cb2) or (c2a,c2b)

Now, equation of the line OC is

y0=c2bc2a(x0) or y=ab× or axby=0


Mathematics

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