Question

The length of the sub-tangent and sub-normal is equal for the curve $y=e^{\mathrm{px}}+\mathrm{px}$ at the point (0, 1), then the value of p is

• A. $\frac{1}{2}$
• B. $-\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $-\frac{1}{4}$

Answer 1

Answer: (A), (B)

$-\frac{1}{2}$

Given that, the length of the sub-tangent and sub-normal is equal for the curve $y=e^{\mathrm{px}}+\mathrm{px}$ at the point (0, 1).
$\frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{pe}}^{\mathrm{px}}+p\mathrm{at}\mathrm{point}\left(0,1\right)=2p\mathrm{Sub}-\mathrm{tangent}=\left(y\frac{\mathrm{dx}}{\mathrm{dy}}\right|,\mathrm{Sub}-\mathrm{normal}=\left(y\frac{\mathrm{dy}}{\mathrm{dx}}\right|\mathrm{Given},\mathrm{sub}-\mathrm{tangent}=\mathrm{sub}-\mathrm{normal}\mathrm{or},\frac{\mathrm{dy}}{\mathrm{dx}}=\pm 1\mathrm{or}2p=\pm 1\mathrm{or},p=\pm \frac{1}{2}.$