Rotate the Axes to Eliminate The $x y$ -Term in the Equation

question 112

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form.
$41 x ^ { 2 } + 18 x y + 41 y ^ { 2 } - 800 = 0$

• A) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 25 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1\)
• B) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 9 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 16 } = 1\)
• C) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1\)
• D) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 9 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 25 } = 1\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 25 } = 1\)

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Definitions:

Phenotype

Characteristic observed in an individual due to the expression of his or her genotype.

Progeria

Severe retardation of growth after the first year accompanied by a senile appearance and death at an early age.

Parturition

The process of childbirth or the act of giving birth.

Physiological Changes

Modifications or adjustments in the functions or activities of the body as a response to various stimuli or environmental conditions.