An Equation of the Form $y ^ { 2 } = 4 p x$

question 22

Multiple Choice

An equation of the form $y ^ { 2 } = 4 p x$ is given. Identify the vertex, value of p, focus, focal diameter, and
endpoints of the latus rectum.
- $$4 y ^ { 2 } = 64 x$$

• A) vertex: \(( 0,0 ) ; p = 4\); focus: \(( 4,0 )\); focal diameter: 16 , endpoints of latus rectum: \(( 4 , - 8 ) ; ( 4,8 )\)
• B) vertex: \(( 0,0 ) ; p = 4\); focus: \(( 0,4 )\); focal diameter: 8 , endpoints of latus rectum: \(( 4 , - 4 ) ; ( 4,4 )\)
• C) vertex: \(( 0,0 ) ; p = 4\); focus: \(( 0,4 )\); focal diameter: 16 , endpoints of latus rectum: \(( 8 , - 4 ) ; ( 8,4 )\)
• D) vertex: \(( 0,0 ) ; p = 4\); focus: \(( 4,0 )\); focal diameter: 8 , endpoints of latus rectum: \(( 4 , - 4 ) ; ( 4,4 )\)

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Definitions:

Burin

A burin is a tool used for engraving or incising hard materials such as stone or metal, typically used in printmaking, jewelry design, and archaeology.

Denisovans

An extinct species or subspecies of archaic humans in the genus Homo, known from DNA evidence and a few fossils found in Siberia.

Mousterian Toolmakers

Prehistoric peoples associated with the Middle Paleolithic period, known for their stone tool technology used by Neanderthals and early modern humans.

Scraper

A tool used for scraping surfaces, typically to remove residue, clean, or make the surface smoother, found in both household and industrial contexts.