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in Co-ordinate geometry by (52.7k points)

If the origin lies in the acute angle between the lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, show that (a1a2 + b1b2)c1c2 < 0.

1 Answer

+1 vote
by (46.6k points)
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Best answer

See Fig.

In ∆OM1M2, ∠M1OM2 is obtuse, that is,

cos∠M1OM2 < 0

So that

OM12 + OM22 -M1M22 < 0

Now, the coordinates of M1 and M2 are

Also,

Substituting these values in Eq. (1), we get

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