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Find the length of the subtangent to the...

Find the length of the subtangent to the curve `x^2y^2=a^4` at `(-a,a).`

Text Solution

Verified by Experts

The correct Answer is:
3
Area of `DeltaOAB = (1)/(2)(1)(8)` = 4 sq. units

The equation of OB is
`y = (1)/(9)x`
Hence, the point E is (C, C/9).
Now, the area of `Delta BDE` is 2 sq. units. Therefore,
`"or " (1)/(2)(1-(C)/(9))(9-C) = 2`
`"or "(9-C)^(2) = 36`
`"or " 9-C = +-6`
or C=3
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