Question

In the curve $y=c{e}^{x/a}$ the
a) Subtangent is constant
b) Subnormal varies as the square of the ordinate

• A. Both a, b are correct
• B. Only b is correct
• C. only a is correct
• D. both a, b are wrong

Answer 1

The correct option is A Both a, b are correct

$y=c{e}^{x/a}\Rightarrow y^{\prime }=\frac{c}{a}{e}^{x/a}$
.
Length of subtangent $=\left|y/y^{\prime }\right|$
$=\left|\frac{c{e}^{x/a}}{\frac{c}{a}{e}^{x/a}}\right|=\left|a\right|$
Hence, subtangent is a constant.
.
Length of subnormal $=|y\times y^{\prime }|$
$=c{e}^{x/a}.\frac{c}{a}{e}^{x/a}={\frac{1}{a}.\left(c{e}^{x/a}\right)}^2=\frac{1}{a}.y^2$
Hence, subnormal varies as square of ordinate.
Hence, both statements are correct.