A curve is such that the mid point of the portion of the tangent intercepted b

Discussion Forum : Differential Equations

Question -

A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets y-axis, lies on the line y = x. If the curve passes through (1, 0), then the curve is

Options:

A .

2 y = x^{2} - x

B .

y = x^{2} - x

C .

y = x - x^{2}

D .

y = 2 (x - x^{2})

Answer: Option C
:
C
The point on y-axis is

(0, y - x \frac{d y}{d x})

According to given condition,

\frac{x}{2} = y - \frac{x}{2} \frac{d y}{d x} \Rightarrow \frac{d y}{d x} = 2 \frac{y}{x} - 1

Putting

\frac{y}{x} = v

we get

x \frac{d v}{d x} = v - 1 \Rightarrow l n ∣ ∣ \frac{y}{x} - 1 ∣ ∣ = l n | x | + c \Rightarrow 1 - \frac{y}{x} = x

(as f(1)=0).

Was this answer helpful ?

Next Question

Discussion Forum : Differential Equations

Submit Your Solution hear: