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If x^(2)+y^(2)+6x-4y-12=0 then find the ...

If `x^(2)+y^(2)+6x-4y-12=0` then find the ragne of 2x+y

Text Solution

Verified by Experts

The correct Answer is:
`[-5sqrt(5)-4,5sqrt(5)-4]`
We have `(x+3)^(2)+(y-2)^(2)=5^(2)`
Let `x=3+5cos theta` and `y=2+5 sin theta`
`therefore 2x+y=-6+2+10cos theta+5 sin theta`
`=-4+5(2cos theta+sin theta)`
Now, `(2cos theta+sin theta)in[-sqrt(5),sqrt(5)]`
`therefore 2x+y=-4+5(2cos theta+sin theta)in[-5sqrt(5),-4,5sqrt(5)-4]`
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