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

question 87

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:

2s Orbitals

2s orbitals are spherical regions around the nucleus of an atom where there is a high probability of finding an electron, belonging to the second energy level.

2p Orbitals

Refers to the second energy level p orbitals in an atom, encompassing three degenerate orbitals (px, py, pz) shaped like dumbbells and oriented perpendicularly to each other.

Protons

Positively charged particles found within the nucleus of an atom, integral to the chemical identity and properties of an element.

Neutrons

Subatomic particles found in the nucleus of an atom, with no electric charge and a mass slightly greater than that of protons.