Prove √(x²+(y-1)²)+√(x²+(y+1)²)=4 is ellipse.

The is a real messy problem. It is an exercise is in exponents.
It can be simplified. Can you clear the radicals from \(\displaystyle \sqrt {{x^2} + {w^2}} + \sqrt {{x^2} - {v^2}} = 4~?\)

If you can, then let \(\displaystyle w = \left( {y - 1} \right)\quad \& \quad v = \left( {y + 1} \right)\).
 
hahalalamummy said:
Prove √(x²+(y-1)²) + √(x²+(y+1)²) = 4 is [an] ellipse
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The suggestion to eliminate the radicals is good, but pka may have misread your post, as the given equation does not contain a difference of squares.


One way to begin is to subtract the second radical from both sides; then, square both sides of the resulting equation and simplify.


Now you have a new equation that contains only one radical. Again, isolate that radical, and then square both sides and simplify.


What you have now contains no radicals, and you can rearrange it into


x^2/3 + y^2/4 = 1


That's the form of an ellipse.


If you get stuck or need confirmation, please post your efforts so far. Cheers :cool:
 
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