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Question

If the slope of one of the lines given by ax2+2hxy+by2=0 is two times the other then

A
8h2=9ab
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B
8h2=9ab2
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C
8h=9ab
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D
8h=9ab2
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Solution

The correct option is A 8h2=9ab
For, b0, the given equation can be written as:-

y2+2hbxy+abx2=0

Let the equations of lines be y+m1x=0 and y+m2x=0

Hence, equation of system of lines becomes:-

(y+m1x)(y+m2x)=0

y2+(m1+m2)xy+m1m2x2=0

Comparing with the given equation, we get:-

m1+m2=2hb and m1m2=ab

Now, m1=2m2

2m2+m2=2hb

m2=2h3b and hence m1=4h3b

Now, m1m2=ab

8h29b2=ab

8h2=9ab

Hence, answer is option-(A).

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