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Question

If the area enclosed between y=mx2 and x=ny2 is 13 sq. units, then m,n can be roots of (where m,n are non zero real numbers)

A
2x2+5x+1=0
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B
2x2+3x2=0
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C
2x2+3x+2=0
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D
2x2+5x1=0
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Solution

The correct option is C 2x2+5x+1=0
y=mx2
y2=m2x4
x=nm2x1/3
x=(1nm2)1/3
y=m1(nm2)2/3
y=m1n2/3m4/3
y=1(n2m)1/3
(1/nm2)1/3
Area=0xnmx2
=[](1/nm2)1/3
=23n(1nm2)13.32m3(1nm2)3×13
=23n1nmm31nm2
=23nm13nm
13=13nm
nm=1
Product of roots =1

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