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If the curves y=2\ e^x and y=a e^(-x) in...

If the curves `y=2\ e^x` and `y=a e^(-x)` intersect orthogonally, then `a=` `1//2` (b) `-1//2` (c) `2` (d) `2e^2`

Text Solution

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`y = 2e^x`
Hence, `dy/dx = 2e^x = m_1`
Also, given that` y= ae^(-x)`
`dy/dx = -ae^(-x) = m_2 `
...
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Knowledge Check

  • If the curve ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 intersect orthogonally, then

    A
    a+b=a'+b'
    B
    a-b=a'-b'
    C
    `(1)/(a)+(1)/(b)=(1)/(a')+(1)/(b')`
    D
    `(1)/(a)-(1)/(b)=(1)/(a')-(1)/(b')`

  • If the curves (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(c^(2))+(y^(2))/(d^(2))=1 intersect orthogonally, then

    A
    `a^(2)-b^(2)=c^(2)-d^(2)`
    B
    `a^(2)-c^(2)=b^(2)-d^(2)`
    C
    `a^(2)b^(2)=c^(2)d^(2)`
    D
    `(1)/(a^(2))+(1)/(b^(2))=(1)/(c^(2))+(1)/(d^(2))`

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