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 (x1−a) 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 Sub−tangent=constantor, Length of a sub−normal=(ydydx∣∣=(yya∣∣=y2(a|∝(square of the ordinate)Equation of the tangent at (x1,y1) is y−y1=y1a(x−x1)This meets the x−axis at a point given by−y1=y1a(x−x1) or x−x1=−a⇒x=x1−aThe curve meets the y−axis at (0, c). ∴(dydx)(0,c)=caSo, the equation of the normal at (0,c) isy−c=−1c/a(x−0)or, ax+cy=c2.