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If real numbers xa n dy satisfy (x+5)^2+...

If real numbers `xa n dy` satisfy `(x+5)^2+(y-12)^2=(14)^2,` then the minimum value of `sqrt(x^2+y^2)` is_________

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The correct Answer is:
1
Let `x+5=14 cos theta` and `y-12=14 sin theta`. Then
`x^(2)+y^(2) = (14 cos theta - 5)^(2) + (14 sin theta +12)^(2)`
`=196+25+144+28(12 sin theta - 5 cos theta )`
`:. sqrt(x^(2)_y^(2))|_("min")=sqrt(365-28xx13)=sqrt(365-364)=1`
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