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  • Can someone explain A curve is such that, intercept cut off by any tangent on y-axis is twice the ordinate of point of tangently, then the curve will be

A curve is such that, intercept cut off by any tangent on y-axis is twice the ordinate of point of tangently, then the curve will be

  • Option 1)

    xy = x + c

  • Option 2)

    xy =c

  • Option 3)

    x^2 y = c

  • Option 4)

    xy^2 = c

Answers (1)

best_answer

As we have learnt,

 

Length of y intercept cut by tangent at P(x,y) -

y-x\frac{dy}{dx}

-

 

 

According to the question -

y-x\frac{dy}{dx} = 2y \\*\Rightarrow -x\frac{\mathrm{d} y}{\mathrm{d} x} = y\Rightarrow xdy + ydx =0 \\*\Rightarrow d(xy) = 0 \\*\Rightarrow xy = c


Option 1)

xy = x + c

Option 2)

xy =c

Option 3)

x^2 y = c

Option 4)

xy^2 = c

Posted by

Himanshu

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