Use the given substitutions to convert the equation to a (u, v) equation with no cross-product term.
-$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0 ;$ use $x = u / \sqrt { 2 } - v / \sqrt { 2 }$ and $y = u / \sqrt { 2 } + v / \sqrt { 2 }$
A) $u ^ { 2 } + v ^ { 2 } = 4$
B) $u ^ { 2 } + 4 v ^ { 2 } = 4$
C) $u ^ { 2 } + 4 v ^ { 2 } = 1$
D) $u ^ { 2 } + 8 v ^ { 2 } = 4$

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The Answer of Use the given substitutions to convert the equation to a (u, v) equation with no cross-product term.
-$5 x ^ { 2 } - 6 x y + 5 y ^ { 2 } - 8 = 0 ;$ use $x = u / \sqrt { 2 } - v / \sqrt { 2 }$ and $y = u / \sqrt { 2 } + v / \sqrt { 2 }$
A) $u ^ { 2 } + v ^ { 2 } = 4$
B) $u ^ { 2 } + 4 v ^ { 2 } = 4$
C) $u ^ { 2 } + 4 v ^ { 2 } = 1$
D) $u ^ { 2 } + 8 v ^ { 2 } = 4$

Use the Given Substitutions to Convert the Equation to a (U