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Find the shortest distance between the parabola `y^2=4ax` and circle `x^2+y^2-24y+128=0.`

Text Solution

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`y^2=4ax`
`x^2+y^2-24y+128=0`
`x^2+(y-12)^2=16`
`y=tx+2at+at^3`
`12=2at+at^3`
when a=1
`t^3+2t-12=0`
`(t-2)(t^2+2t+6)=0`
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