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Question

Condition for which the slope of a line represented by ax2+2hxy+by2=0 is square of the other is ,

A
ab(a+b6h)+8h3=0
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B
ab(a+b6h)=8h3
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C
ab(a+b+6h)+8h3=0
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D
None of thses
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Solution

The correct option is A ab(a+b6h)+8h3=0
According to question.......
ax2+2hxy+by2=0ifwehavetwoliney=m1x&y=m2xandthisisthesquareoftheother,m2=m12then,y=m1x&y=m12x(wehavetwostraightlineequnknow,(ym1x)(ym12x)=0y2x(m1+m12)+m13x2=0Now,compare:m1+m12=2hb,&m13=ab(m1+m12)3=8h3b3m13+m16+3m31(m1+m12)=8h3b3ab+a2b2+3(ab).(2hb)=8h3b3ab+a2b2+8h3b3=6ahb2ab[1+ab]+8h3b3=6ahb2a(a+b)b2+8h3b3=6ahb2a(a+b)ah+8h3bah=6a+bh+8h2ab=6ab(a+b)+8h3h(ab)=6ab(a+b)+8h3=6h(ab)ab(a+b6h)8h3=0So,thatthecorrectoptionisA.

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