An Equation of a Parabola Is Given $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

question 122

Multiple Choice

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
focus and the equation of the directrix.
- $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

• A) \(\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )\)
• focus: \(\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;\) directrix \(: y = - \frac { 3 } { 2 }\)
• B) \(( x + 14 ) ^ { 2 } = - 40 \left( y + \frac { 13 } { 40 } \right)\)
• focus: \(\left( - 14 , - \frac { 387 } { 40 } \right) ;\) directrix: \(y = - \frac { 413 } { 40 }\)
• C) \(\left( x - \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )\)
• focus: \(\left( \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;\) directrix: \(y = - \frac { 3 } { 2 }\)
• D) \(\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y - 4 )\)
• focus: \(\left( - \frac { 7 } { 2 } , \frac { 3 } { 2 } \right)\); directrix: \(y = \frac { 13 } { 2 }\)

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Definitions:

Renal Mechanisms

Renal Mechanisms pertain to the various functions and processes carried out by the kidneys, vital for maintaining body fluid balance, electrolyte levels, and filtering waste from the bloodstream.

Body Fluids

Liquids within the human body that perform important functions, including blood, saliva, urine, and sweat.

Hormone Levels

The concentration of hormones within the bloodstream, influencing various bodily functions and processes.

Kidney Function

The role played by the kidneys in filtering waste, controlling the body's fluid balance, and regulating electrolytes, blood pressure, and red blood cell production.