Question

A curve is represented parametrically by the equations

x = t + e^at and y = –t + e^at when t О R and a > 0. If the curve touches the axis of x at the point A, then the coordinates of the point A are

• A. (1, 0)
• B. (2e, 0)
• C. (1/e, 0)
• D. (e, 0)

Answer 1

Answer: (B)

(2e, 0)

Answer 2

let it be (t₁ 0) so 0 = – t₁ + $e^{at_{1}}$.........(i)

Now $\frac{dy}{dx}$ = 0 ̃ $\frac{dy}{dt}$ = 0 ̃ – 1 + a$e^{at_{1}}$ = 0

̃ $e^{at_{1}}$ = $\frac{1}{a}$ ....(ii)

from (i) & (ii) t₁ = $\frac{1}{a}$ Hence $e^{a.\frac{1}{a}}$ =$\frac{1}{a}$̃ $\frac{1}{a}$ = e

Hence x = $\frac{1}{a}$ +$\frac{1}{a}$ so x = $\frac{2}{a}$ = 2e

pt A (2e, 0)

e = $\sqrt{1–b^{2}/a^{2}}$