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
Answer: Option C
:
C
The point on y-axis is (0,y−xdydx)
According to given condition,
x2=y−x2dydx⇒dydx=2yx−1
Putting yx=v we get
xdvdx=v−1⇒ln∣∣yx−1∣∣=ln|x|+c⇒1−yx=x (as f(1)=0).
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:
C
The point on y-axis is (0,y−xdydx)
According to given condition,
x2=y−x2dydx⇒dydx=2yx−1
Putting yx=v we get
xdvdx=v−1⇒ln∣∣yx−1∣∣=ln|x|+c⇒1−yx=x (as f(1)=0).
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