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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?
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
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
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