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Question

The equations of the assymptotes of the hyperbola 3x2+10xy+8y2+14x+22y+7=0 are .

A
3x2+10xy+8y2+14x+22y7=0
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B
3x2+10xy+8y2+14x+22y=0
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C
3x2+10xy+8y2+14x+22y+14=0
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D
3x2+10xy+8y2+14x+22y+15=0
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Solution

The correct option is D 3x2+10xy+8y2+14x+22y+15=0
As the equation of the assymptotes and a hyperbola only differs by a constant,
Hence, the equation of the assymptotes will be:
3x2+10xy+8y2+14x+22y+k=0 ...(i)
k is chosen in such a manner that (i) represents the pair of the straight lines.
Hence, if ax2+2hxy+by2+2gx+2fy+c=0 representsa pair of straight lines, then abc+2fgh−af2−bg2−ch2=0⇒3×8×k+2×7×11×5−3×121−8×49−k×25=0⇒k=15
Hence, the combined equation of the assymptotes is :

3x2+10xy+8y2+14x+22y+15=0

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