A curve is represented parametrically by the equations x=t+e text at and y=-t+e text at when t ∈ R and a0. If the curve touches the axis of x at the point A, then the coordinates of the point A are

Question

A curve is represented parametrically by the equations x=t+e text at and y=-t+e text at when t ∈ 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) (1 / e , 0) (C) ( e , 0) (D) (2 e , 0)

Tardigrade Admin · Accepted Answer

( dx / dt )=1+ ae at ; ( dy / dt )=-1+ ae at ; ( dy / dx )=(-1+ ae at /1+ ae at ) at the point A, y=0 and (d y/d x)=0 for some t=t1 ∴ ac at 1=1....(1) also 0=- t 1+ e at 1 ; ∴ e at 1= t 1.....(2), putting this value in (1) we get, at 1=1 ⇒ t1=(1/a); (1) ae =1 ⇒ a=(1/e) hence x A = t 1+ e at 1= e + e =2 e ⇒ A ≡(2 e , 0)

Q. A curve is represented parametrically by the equations $x = t + e^{at}$ and $y = - t + e^{at}$ when $t \in R$ and $a > 0$ . If the curve touches the axis of $x$ at the point $A$ , then the coordinates of the point $A$ are

$(1, 0)$

$(1/ e, 0)$

$(e, 0)$

$(2 e, 0)$

Q. A curve is represented parametrically by the equations x=t+eat and y=−t+eat when t∈R and a>0. If the curve touches the axis of x at the point A, then the coordinates of the point A are

(1,0)

(1/e,0)

(e,0)

(2e,0)

Q. A curve is represented parametrically by the equations $x = t + e^{at}$ and $y = - t + e^{at}$ when $t \in R$ and $a > 0$ . If the curve touches the axis of $x$ at the point $A$ , then the coordinates of the point $A$ are

$(1, 0)$

$(1/ e, 0)$

$(e, 0)$

$(2 e, 0)$