For What Value Of $a$ Does the Equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$

question 50

Multiple Choice

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$ represent a circle with center $( 3 , - 2 )$ ? When $a$ assumes this value, what is the radius of the circle?

• A) \(\quad a = 4 , \quad\) radius \(= 5\)
• B) \(\quad a = 7 , \quad\) radius \(= 6\)
• C) \(\quad a = 6 , \quad\) radius \(= 4\)
• D) \(\quad a = 5 , \quad\) radius \(= 5\)
• E) \(\quad a = 5 , \quad\) radius \(= 3\)

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Definitions:

Equilibrium

Equilibrium in economics is the point where supply equals demand for a product, resulting in stable prices and volume of sales.

Efficient Portfolio

Provide the highest expected return for any degree of risk. The efficient portfolio is that which provides the lowest degree of risk for any expected return.

Expected Return

Expected Return is the anticipated profit or loss a portfolio generates over a specific period, based on historical or forecasted performance.

Risk

The exposure to uncertainty and the potential for losing something of value, in finance typically referring to the uncertainty in investment returns.