Consider the equation. $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ Without calculating,explain how to rewrite the equation so that it does not have an $$x y$$ -term.

A)To rewrite the equation $$6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$$ so that it does not have an $x y$ -term,you can solve for $y$ in terms of $x$ by completing the square or using the Quadratic Formula.
B)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it does not have an $x y$ -term,you can solve for $x$ in terms of $y$ by completing the square or using the Quadratic Formula.
C)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $y$ $y$ in terms of $x$ by taking square root or using the Quadratic Formula.
D)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $x$ in terms of $y$ by completing the square or using the Quadratic Formula.
E)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $y$ in terms of $x$ by completing the square or using the Quadratic Formula.

Question

Consider the equation.​ $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ ​ Without calculating,explain how to rewrite the equation so that it does not have an $$x y$$ -term.
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A)To rewrite the equation $$6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$$ so that it does not have an $x y$ -term,you can solve for $y$ in terms of $x$ by completing the square or using the Quadratic Formula.
B)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it does not have an $x y$ -term,you can solve for $x$ in terms of $y$ by completing the square or using the Quadratic Formula.
C)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $y$ $y$ in terms of $x$ by taking square root or using the Quadratic Formula.
D)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $x$ in terms of $y$ by completing the square or using the Quadratic Formula.
E)To rewrite the equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$ so that it has an $x y$ -term,you can solve for $y$ in terms of $x$ by completing the square or using the Quadratic Formula.

Quizplus · Accepted Answer

To eliminate the $xy$ term, you can rotate the coordinate system or use a substitution that diagonalizes the quadratic form, which is akin to completing the square or using the quadratic formula to express one variable in terms of the other.

Consider the Equation 6x2−3xy+6y2−25=06 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 06x2−3xy+6y2−25=0

Consider the Equation $6 x ^ { 2 } - 3 x y + 6 y ^ { 2 } - 25 = 0$