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If the angle between the normal to the p...

If the angle between the normal to the parabola `y^(2)=4ax` at point P and the focal chord passing through P is `60^(@)`, then find the slope of the tangent at point P.

Text Solution

Verified by Experts


By property,
SP=ST=SN.
Given that `angleSPN=60^(@)`
`:." "angleSPT=30^(@)`
Since `ST=SP,anglePTS=30^(@)`
Therefore, slope of tangent `=tan30^(@)=(1)/(sqrt(3))`.
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Knowledge Check

  • The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

    A
    ` tx+y=2at+at^(3)`
    B
    ` x+ty=2at+at^(3)`
    C
    `tx-y=at +2at^(3)`
    D
    `x-ty=at+2at^(3)`

  • The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

    A
    `t`
    B
    `(1)/(t)`
    C
    `-t`
    D
    `-(1)/(t)`

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