Question

The curves whose subtangents are proportional to the

abscissas of the point of tangency (the proportionality factor

is equal to k) is-

• A. y^k = Cx
• B. y^k = Cx²
• C. y^k/2 = Cx³
• D. None

Answer 1

Answer: (A)

y^k = Cx

Answer 2

Subtangent = y $\frac{dx}{dy}$ so according to the given condition

y $\frac{dx}{dy}$ = kx

Ž $\frac{dx}{x}$ = k $\frac{dy}{y}$ Ž log A + log |x| = k log |y|

Ž A |x| = |y|^k

Ž y^k = ± Ax = Cx.