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Question

The angle of intersection of the normals at the point (52,32) of the curves x2y2=8 and 9x2+25y2=225 is

A
0
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B
π2
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C
π3
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D
π4
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Solution

The correct option is B π2
x2y2=8
dydx=xy
1dy/dx=yx

At the point (52,32),
1dy/dx=3/25/2=35

Also, 9x2+25y2=225
or 18x+50ydydx=0
or dydx=9x25y or dxdy=25y9x

At the point (52,32),
dxdy=25×3/29(5/2)=159=53

Since, the product of the slopes is 1, the normals cut orthogonally, i.e., the required angle is equal to π2.

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