Find the Vertex, Focus, and Directrix of the Parabola $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

question 415

Multiple Choice

Find the vertex, focus, and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

• A)Vertex: \(\left( - 5 , \frac { 5 } { 2 } \right)\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• B)Vertex: \(\left( \frac { 5 } { 2 } , - 5 \right)\) ; Focus: \(\left( - 5 , \frac { 3 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• C)Vertex: \(\left( \frac { 5 } { 2 } , - 5 \right)\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• D)Vertex: \(\left( - 5 , \frac { 5 } { 2 } \right)\) ; Focus: \(\left( - 5 , \frac { 3 } { 2 } \right)\) ; Directrix: \(y = \frac { 7 } { 2 }\)
• E)Vertex: \(( 0,0 )\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 7 } { 2 }\)

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Definitions:

Sodium-Potassium Pump

A cell membrane protein that uses ATP to move sodium ions out of the cell and potassium ions into the cell, essential for cellular function.

Plasma Membrane

The phospholipid bilayer that surrounds cells, controlling the movement of substances in and out of the cell, thereby maintaining its internal environment.

Actively Transports

The process of transporting materials through cellular barriers against the direction of concentration differences, necessitating the use of energy.

Active Transport

The migration of molecules from a lower concentration zone to a higher concentration zone across a cell's membrane, an action that requires energy.