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For a curve $y = ⨍ (x),$ if a, b, l, m represent the lengths of tangent, normal, subtangent, subnormal respectively then $a^{2} : b^{2} =$

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l : m

$l^{2} : m^{2}$

$m^{2} : l^{2}$

m : l

answer is A.

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Detailed Solution

$a = \frac{y_{1} \sqrt{1 + m^{2}}}{m} b = y_{1} \sqrt{1 + m^{2}} \frac{a}{b} = \frac{1}{m} l = \frac{y_{1}}{m} m = y_{1} \cdot m \frac{l}{m} = \frac{1}{m^{2}} = \frac{a^{2}}{b^{2}}$

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