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if y^(2)(y^(2)-6)+x^(2)-8x+24=0, then ma...

if `y^(2)(y^(2)-6)+x^(2)-8x+24=0`, then maximum value of `sqrt(y^(4)+x^(2))` is

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The correct Answer is:
6

`x^(2)+y^(4)-8x6y^(2)+24=0`
Let `y^(2)=1`
`x^(2)+t^(2)-8x-6t+24=0`
Equation of a circle in `x-t` coordinate system with centre `(4,3)`& radius `=1`
`sqrt(y^(4)+x^(2))=sqrt(t^(2)+x^(2))implies` distance of any `pt(x,t)` on circle from origin
`M=OQ=OC+r=6`
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