Applications of Derivatives Question - None

Question

Ex. 24(B): If the length of subtangent to the curve y^2 = \frac{x^2}{k|x|} + 1 at the point (-2, 2) is \frac{16}{|k|}\frac{}{}, then the value of k is

Accepted Answer

Solution:

For a curve y = f(x), the length of subtangent at a point is \left|\frac{y}{dy/dx} ight|.

Given curve: y^2 = \frac{x^2}{k|x|} + 1

At point (-2, 2): 4 = \frac{4}{-2k} + 1

Solving: 3 = \frac{-2}{k} \Rightarrow k = -\frac{2}{3}

The length of subtangent = \frac{16}{|k|}\frac{}{} matches with values corresponding to k = 2 ext{ or }k = -2

∴ Answer: (r, s)

Question:

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