Q.

If the tangent line at the point p(t) to the curve x=f(t),y=g(t) makes an angle ψ with ox→ then f1(t):g1(t)=

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a

tanψ:cosψ

b

cos ψ:sin ψ

c

sinψ:cosψ

d

cosec ψ: tanψ

answer is B.

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Detailed Solution

We have dydx=dy/dtdx/dt=g1(t)f1(t) And dydx=Tan ψ=sin ψcos ψ=g'(t)f'(t)⇒f'(t):g'(t)=cosψ:sinψ .

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If the tangent line at the point p(t) to the curve x=f(t),y=g(t) makes an angle ψ with ox→ then f1(t):g1(t)=