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Question

The straight line joining the origin to the other two points of intersection of the curve whose equations are ax2+2hxy+2gx+by2=0andax2+2hxy+by2+2gx=0 will be at right angle if

A
g(a+b)g(a+b)=0
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B
gg=abab
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C
gg=(ab)(ab)
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D
none of these
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Solution

The correct option is B g(a+b)g(a+b)=0
Given eq of curves
ax2+2hxy+2gx+by2=0----(1)
ax2+2hxy+2gx+by2=0----(2)
1=ax2+2hxy+by22gx
Putting in eq (1)
ax2+2hxy+2gx(ax2+2hxy+by22gx)+by2=0
ax2+2hxyg(ax2+2hxy+by2g)+by2=0
agx2+2hgxygax22ghxygby2+bgy2=0
x2(agag)+y2(bgbg)+2xy(hggh)=0
Here by perpendicularlly
agag+bgbg=0
(a+b)gg(a+b)=0
g(a+b)g(a+b)=0


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