Find an Equation for the Orthogonal Trajectories of the Given $8 x ^ { 2 } + y = C$

question 13

Multiple Choice

Find an equation for the orthogonal trajectories of the given family of curves. $8 x ^ { 2 } + y = C$

• A) \(y - \ln x ^ { 16 } = C\)
• B) \(y - x e ^ { 1 / 16 } = C\)
• C) \(y - \ln x ^ { 1 / 6 } = C\)
• D) \(\ln y - x ^ { 1 / 6 } = C\)

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Definitions:

Inferior Vena Cava

A large vein that carries deoxygenated blood from the lower and middle parts of the body back to the right atrium of the heart.

Left Atrium

The upper left chamber of the heart, which receives oxygenated blood from the lungs and pumps it into the left ventricle.

Angina Pectoris

A condition characterized by chest pain due to reduced blood flow to the heart muscle, often indicative of coronary heart disease.

Myocardial Infarction

A medical emergency commonly known as a heart attack, caused by the interruption of blood flow to a part of the heart, leading to heart muscle damage.