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Question

In the curve y=cex/a, the

A
The length of a sub-tangent is constant
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B
The length of a sub-normal varies as the square of the ordinate
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C
tangent at (x1,y1) on the curve intersects the x-axis at a distance of (x1a) from the origin.
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D
equation of the normal at the point where the curve cuts y-axis is cy+ax=c2
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Solution

The correct options are
A The length of a sub-tangent is constant
B The length of a sub-normal varies as the square of the ordinate
C tangent at (x1,y1) on the curve intersects the x-axis at a distance of (x1a) from the origin.
D equation of the normal at the point where the curve cuts y-axis is cy+ax=c2
We have, y=cex/a
dydx=caex/a=1ayor, (ydy/dx∣ ∣=(a|=constantor, The length of a Subtangent=constantor, Length of a subnormal=(ydydx=(yya=y2(a|(square of the ordinate)Equation of the tangent at (x1,y1) is yy1=y1a(xx1)This meets the xaxis at a point given byy1=y1a(xx1) or xx1=ax=x1aThe curve meets the yaxis at (0, c). (dydx)(0,c)=caSo, the equation of the normal at (0,c) isyc=1c/a(x0)or, ax+cy=c2.

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