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Find the lengths of subtangent and subno...

Find the lengths of subtangent and subnormal at a point on the curve `y=bsin(x/a)`

Text Solution

Verified by Experts

The correct Answer is:
`|(b^(2))/(2a).sin.(2x)/(a)|`
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Find the length of subtangent, subnormal at a point on the curve x=a(cost+sint), y=a(sint-tcost)

Find the lengths of subtangent, sub normal at a point t on the curve x=a(cost+tsint), y=a(sint-tcost) .

Knowledge Check

  • The length of the subtangent at any point x_1,y_1 on the curve y=5^x

    A
    `5x_1`
    B
    `y_(1)5x_1`
    C
    `log_e5`
    D
    `1/log_e5`

  • The sum of the lengths of the subtangent and subnormal at theta=pi//3 on the cycloid x=a(theta-sintheta),y=a(1-costheta) is

    A
    `2a`
    B
    `2sqrt(a)`
    C
    `2a//sqrt(3)`
    D
    `a//sqrt(3)`

  • If T is the length of the subtangent drawn at any point on the curve 3y^(2) = 4x^(3) and N is the length of the subnormal at the same point, the (3T)^(2) =

    A
    `4 N^(2)`
    B
    4N
    C
    2N
    D
    `8N^(2)`

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