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suchintan mondal Grade: 12
        

The tangent at a point P(x,y) on a curve meets the axes at M and N such that P divides MN internally in the ratio 2:1. Then find the equation of the curve?

7 years ago

Answers : (1)

Ramesh V
70 Points
										

let eqn of line L: x/a + y/b = 1


where a, b are X,Y intercepts of line L


so, dy/dx = -1/a


and the point P which divides MN internally in the ratio 2:1


so x=a/3 and y=2b/3


on substiting in diff. eqn , we have


 


dy/dx = -y/2x


i.e (1/y) dy  = -(1/2x) .dx


ln y = -1/2lnx +lnC where lnC is constant


so eqn. of curve is :  y=(kx)-1/2

7 years ago
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