List the Intercepts and Type(s) of Symmetry, If Any $$16 x ^ { 2 } + y ^ { 2 } = 16$$

question 213

Multiple Choice

List the intercepts and type(s) of symmetry, if any.
- $$16 x ^ { 2 } + y ^ { 2 } = 16$$

• A) intercepts: \(( 4,0 ) , ( - 4,0 ) , ( 0,1 ) , ( 0 , - 1 )\)
• symmetric with respect to \(x\)-axis and \(y\)-axis
• B) intercepts: \(( 1,0 ) , ( - 1,0 ) , ( 0,4 ) , ( 0 , - 4 )\)
• symmetric with respect to \(x\)-axis and \(y\)-axis
• C) intercepts: \(( 1,0 ) , ( - 1,0 ) , ( 0,4 ) , ( 0 , - 4 )\)
• symmetric with respect to \(\mathrm { x }\)-axis, \(\mathrm { y }\)-axis, and origin
• D) intercepts: \(( 4,0 ) , ( - 4,0 ) , ( 0,1 ) , ( 0 , - 1 )\)
• symmetric with respect to the origin

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Definitions:

Strictly Convex

A term often used in mathematics and economics to describe a curve or function that curves away from the origin more sharply than a straight line, indicating increasing marginal effects.

Perfect Substitutes

Perfect substitutes are products or services that can be used in exactly the same way, offering the same utility to consumers, thus one can replace the other without loss of value or function.

Homothetic Preferences

Consumer preferences that are consistent or proportionate across different scales or levels of consumption, indicating a straight line through the origin in a utility function graph.

Quasilinear Preferences

Preferences where utility is a linear function of one good, making the consumer's marginal rate of substitution between goods independent of the level of consumption of that good.