Use Axis of Rotation Formulas for X and Y to Transform

question 14

Multiple Choice

Use axis of rotation formulas for x and y to transform the quadratic equation to an equation in (u, v) coordinates with no
cross-product term.
- $$2 x ^ { 2 } + 2 \sqrt { 3 } x y + 4 y ^ { 2 } - 8 = 0$$

• A) \(\frac { \mathrm { u } ^ { 2 } } { 8 } + \frac { 5 \mathrm { v } ^ { 2 } } { 8 } = 1\)
• B) \(\frac { 5 \mathrm { u } ^ { 2 } } { 8 } + \frac { \mathrm { v } ^ { 2 } } { 8 } = 1\)
• C) \(\frac { 2 u ^ { 2 } } { 8 } + \frac { v ^ { 2 } } { 8 } = 1\)
• D) \(\frac { 3 \mathrm { u } ^ { 2 } } { 16 } + \frac { \mathrm { v } ^ { 2 } } { 16 } = 1\)

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Definitions:

Transduction

The process of converting one form of energy into another, a term commonly used in biology, physics, and sensory processes.

Neural Signals

Electrical impulses and chemical signals transmitted by neurons to communicate information throughout the nervous system.

Light Energy

The form of energy that is visible to the human eye and is responsible for the sense of sight.

Pupillary Opening

The adjustable opening at the center of the iris in the eye, which controls the amount of light that enters the eye.