Convert the Equation to the Standard Form for a Hyperbola $$\mathrm { y } ^ { 2 } - 16 \mathrm { x } ^ { 2 } - 4 \mathrm { y } + 64 \mathrm { x } - 76 = 0$$

question 92

Multiple Choice

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
- $$\mathrm { y } ^ { 2 } - 16 \mathrm { x } ^ { 2 } - 4 \mathrm { y } + 64 \mathrm { x } - 76 = 0$$

• A) \(\frac { ( y - 2 ) ^ { 2 } } { 16 } - ( x - 2 ) ^ { 2 } = 1\)
• B) \(\frac { ( x - 2 ) ^ { 2 } } { 16 } - ( y - 2 ) ^ { 2 } = 1\)
• C) \(\frac { ( y - 4 ) ^ { 2 } } { 16 } - ( x - 4 ) ^ { 2 } = 1\)
• D) \(( x - 2 ) ^ { 2 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1\)

---

Definitions:

Thermoreceptors

Thermoreceptors are sensory receptors that detect changes in temperature, enabling the sensation of warmth or cold.

Ciliary Muscle

A ring of smooth muscle in the eye's middle layer that changes the shape of the lens for focusing.

Suspensory Ligaments

Fibrous tissues that connect the lens of the eye to the ciliary body, adjusting the lens shape for focusing.

Fovea

A small depression in the retina of the eye where visual acuity is highest, due to the high density of cones, and no rods.