Prove that angle between one of the lines given by ax2 -8203-2hxy-by2-0 and one of the lines ax2 -8203-2hxy-by2-k-x2- -8203-y2-0 is equal to the angle between other two lines of the system-

Let L1 nbsp;and L2 nbsp;be one pair and L3 nbsp;and L4 nbsp;be the other pair of lines. nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nb ...

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Standard XII

Mathematics

Condition of Concurrency of 3 Straight Lines

prove that an...

Question

prove that angle between one of the lines given by ax²+2hxy+by²=0 and one of the lines ax²+2hxy+by²+k(x²+y²)=0 is equal to the angle between other two lines of the system.

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Solution

Let L1 and L2 be one pair and L3 and L4 be the other pair of lines.

If the angle between L1 and L3 is equal to the angle between L2 and L4 then pair of bisectors of L1 and L2 would be same as that of L3 and L4. Pair of bisectors of L3 and L4 is

x2–y2/(a+k)–(b+k) = xy/h

⇒ x2–y2/a–b = xy/h

Which is the same as the bisector pair of L1 and L2.

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prove that angle between one of the lines given by ax2​+2hxy+by2=0 and one of the lines ax2​+2hxy+by2+k(x2+​y2)=0 is equal to the angle between other two lines of the system.

prove that angle between one of the lines given by ax²+2hxy+by²=0 and one of the lines ax²+2hxy+by²+k(x²+y²)=0 is equal to the angle between other two lines of the system.