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If (x^2)/4+(y^2)/9=1, then find the rang...

If `(x^2)/4+(y^2)/9=1,` then find the range of `2x+y`

Text Solution

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we have `((x)/(2))^(2)+((y)/(3))^(2)=1`
Put `x=2cos theta` and `y=3 sin theta`
`therefore 2x+y=4cos theta+3sin theta`
`therefore 2x+y=4cos theta+3 sin theta`
`4cos theta+3sin theta in [-sqrt(4^(2)+3^(2)),sqrt(4^(2)+3^(2))]` or `[-5,5]`
`therefore 2x+y in [-5,5]`
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