Find the Vertex and Focus of the Parabola Below $$y ^ { 2 } + 6 y - 8 x + 20 = 0$$

question 111

Multiple Choice

Find the vertex and focus of the parabola below.
$$y ^ { 2 } + 6 y - 8 x + 20 = 0$$

• A) Vertex: \(\left( - \frac { 11 } { 8 } , 3 \right)\)
• Focus: \(\left( \frac { 5 } { 8 } , 3 \right)\)
• B) Vertex: \(\left( \frac { 11 } { 8 } , - 3 \right)\)
• Focus: \(\left( \frac { 27 } { 8 } , - 3 \right)\)
• C) Vertex: \(\left( \frac { 11 } { 8 } , - 3 \right)\)
• Focus: \(\left( \frac { 75 } { 8 } , - 3 \right)\)
• D) Vertex: \(\left( - \frac { 11 } { 8 } , 3 \right)\)
• Focus: \(\left( \frac { 53 } { 8 } , 3 \right)\)
• E) Vertex: \(\left( - \frac { 11 } { 8 } , - 3 \right)\)
• Focus: \(\left( \frac { 53 } { 8 } , - 3 \right)\)

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Definitions:

Oxidation

A chemical reaction involving the loss of electrons from a molecule, which often results in the production of energy.

Citric Acid Cycle

A key metabolic pathway that occurs in the mitochondria, involving a series of chemical reactions used by all aerobic organisms to generate energy through the oxidation of acetate.

NADH

Nicotinamide adenine dinucleotide (reduced form), a coenzyme found in all living cells that plays a critical role in energy production through cellular respiration.

Citric Acid Cycle

A series of chemical reactions used by all aerobic organisms to generate energy through the oxidation of acetate derived from carbohydrates, fats, and proteins into carbon dioxide.