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Prove that for thetainR, the line y=(x-1...

Prove that for `thetainR`, the line `y=(x-11)costheta-cos3theta` is always normal to the parabola `y^(2)=16x`.

Text Solution

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The slope of the given line is m `=costheta`.
Also, normal to parabola `y^(2)=16x` having slope m is
`y=mx-8m-4m^(3)`
`:." "y=xcostheta-8costheta-4cos^(3)theta`
`:." "y=xcostheta-11costheta+3costheta-4cos^(3)theta`
`:." "y=(x-11)costheta-cos3theta`
so, this line is always normal to parabola `y^(2)=16x`.
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