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

question 145

Multiple Choice

Use the given substitutions to convert the equation to a (u, v) equation with no cross-product term.
- $7 \mathrm { x } ^ { 2 } + 5 \sqrt { 3 } \mathrm { xy } + 2 \mathrm { y } ^ { 2 } - 31 = 0 ;$ use $x = \sqrt { 3 } \mathrm { u } / 2 - \mathrm { v } / 2$ and $\mathrm { y } = \mathrm { u } / 2 + \sqrt { 3 } \mathrm { v } / 2$

• A) \(\frac { 19 } { 2 } u ^ { 2 } - 2 v ^ { 2 } = 1\)
• B) \(\frac { 19 } { 62 } \mathrm { u } ^ { 2 } + \frac { 1 } { 62 } \mathrm { v } ^ { 2 } = 1\)
• C) \(\frac { 19 } { 62 } u ^ { 2 } - \frac { 1 } { 62 } v ^ { 2 } = 1\)
• D) \(\frac { 19 } { 2 } u ^ { 2 } - \frac { 1 } { 62 } v ^ { 2 } = - 1\)