If , for some , prove that [1+ ( d y d x )^ 2 ]^ 3 2 d^ 2 y d x^ 2 is a constant…

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

15. If

(x-a)^{2}+(y-b)^{2}=c^{2}

, for some

c>0

, prove that

\frac{\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{\frac{3}{2}}}{\frac{d^{2} y}{d x^{2}}}

is a constant independent of

a

and

b

.

Related theory

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