Find the Center,vertices and Foci of the Hyperbola $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

question 31

Multiple Choice

Find the center,vertices and foci of the hyperbola.​ $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$ ​

• A)Center: (0,0) Vertices: \(( \pm 4,0 )\)
• Foci: \(( \pm \sqrt { 41 } , 0 )\)
• B)Center: (0,0) Vertices: \(( 0 , \pm 4 )\)
• Foci: \(( 0 , \pm \sqrt { 41 } )\)
• C)Center: \(( 16,25 )\) Vertices: \(( \pm 5,0 )\)
• Foci: \(( \pm \sqrt { 41 } , 0 )\)
• D)Center: (0,0) Vertices: \(( \pm 5,0 )\)
• Foci: \(( \pm \sqrt { 41 } , 0 )\)
• E)Center: \(( 16,25 )\) Vertices: \(( \pm 4,0 )\)
• Foci: \(( \pm \sqrt { 41 } , 0 )\)

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Definitions:

Counter Structure

A programming construct used to store the number of occurrences or iterations, often used in loops or to track events.

Retains Accum

A function or method in PLCs or similar systems that allows the accumulation of data or values to be retained even after power loss or system restart.

Rung Goes False

In ladder logic programming for PLCs, this refers to the condition where the conditions for a particular rung are not met, leading to a false or "off" state.

CTD Counter

A "Count Down" counter that decreases its value by one each time it is triggered, often used in PLC programming.