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Determine the value of p such that the s...

Determine the value of p such that the subtsngent and subnormal are equal for the curve `y=e^(px)+px` at the point (0,1).

A

`(L_(ST))/(2010)=(2010)/(L_(SN))`

B

`|(L_(T))/(L_(N))sqrt((L_(SN))/(L_(ST)))|="constant"`

C

`1-L_(ST)L_(SN)=(2000)/(2010)`

D

`((L_(T)+L_(N))/(L_(T)-L_(N)))^(2)=(L_(ST))/(L_(SN))`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`L_(ST)=|(y)/(m)|,L_(SN)=|ym|`
`L_(T)=|(4sqrt(1+m^(2)))/(m)|.L_(N)=|ysqrt(1+m^(2))|`
where `m=(dy)/(dx)` at point `P=(x,y)` on the curve `y = f(x)`
Now `(L_(ST))/(L_(SN))=(1)/(m^(2))=((L_(T))/(L_(N)))^(2) and L_(ST)L_(SN)=y^(2)`
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