Find the Vertex, the Focus, and the Directrix of the Parabola

question 165

Multiple Choice

Find the vertex, the focus, and the directrix of the parabola.
- $$2 x ^ { 2 } + 20 x - y + 53 = 0$$

• A) Vertex: \(( - 5,0 )\); Focus: \(( - 5,5 )\); Directrix: \(x = 1\)
• B) Vertex: \(\left( - 5 , - \frac { 24 } { 17 } \right)\); Focus: \(\left( - 5 , \frac { 23 } { 8 } \right) ;\) Directrix: \(x = \frac { 25 } { 8 }\)
• C) Vertex: \(( - 5,3 )\); Focus: \(( - 5,11 )\); Directrix: \(x = 5\)
• D) Vertex: \(( - 5,3 )\); Focus: \(\left( - 5 , \frac { 25 } { 8 } \right)\); Directrix: \(y = \frac { 23 } { 8 }\)

---

Definitions:

Useful Life

The estimated duration a fixed asset is expected to be economically utilisable by the business before it's fully depreciated.

Goodwill

An intangible asset representing the value of a company's brand, customer relationships, employee relations, and other non-physical assets.

Intangible Asset

An asset that lacks physical substance but is still valuable because of its potential economic benefits, such as patents or trademarks.

Amortized

The process of spreading out a loan or intangible asset cost over a fixed period in regular installments, covering interest and principal payments.