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Prove that the equation of the normal to...

Prove that the equation of the normal to `x^(2/3)+y^(2/3)=a^(2/3)` is `ycostheta-xsintheta=acos2theta,` where `theta` is the angle which the normal makes with the axis of `xdot`

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Prove that the equation of the normal to x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) is y cos theta-x sin theta=a cos2 theta where theta is the angle which the normal makes with the axis of x.

The normal at theta of the circle x^(2)+y^(2)=a^(2) is

Knowledge Check

  • The equation of normal to the curve x^(2//3)+y^(2//3)=a^(2//3) at (asin^(3) theta, a cos^(3) theta) is

    A
    `sin theta x-cos theta y=a sin^(4) theta-cos^(4)theta`
    B
    `sin thetax+cos thetay=a sin^(4) theta+a cos^(4)theta`
    C
    `sin thetax-cos thetay=asin^(4) theta+a cos^(4) theta`
    D
    None of the above

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