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Question

A: Length of sub-normal to y=4x2 at (1,4).
B: Length of sub-normal to y=x3+1 at (1,2).
C: Length of sub-tangent to xy=12 at (3,4).
D: Length of normal to x3+y3=6xy at (3,3).
The ascending order of the above values is

A
DCBA
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B
ABCD
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C
CDBA
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D
ABDC
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Solution

The correct option is C CDBA
(A) y=8x
y|x=1=8
SN=|ym|=4×8=32

(B) y=3x2
y|x=1=3
SN=|ym|=3×2=6

(C) y=12x2
y|x=3=43
ST=(ym)=(4+34)=3

(D) x2+y2y=2(xy+y)
9+9y=2(3y+3)3+3y=2y+2y=1
N=y1+m2=32

Ascending order of values
C<D<B<A
Hence, option C.

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