Show That the Curves Are Orthogonal $y ^ { 2 } + x ^ { 2 } = 1 \text { and } x y = 2$

question 41

Essay

Show that the curves are orthogonal.
- $y ^ { 2 } + x ^ { 2 } = 1 \text { and } x y = 2$

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Definitions:

Quantifier Negation

The act of negating the quantifier in a logical statement, which changes the scope or range of the statement.

Universal Generalization

A conclusion drawn about all things in a certain category, based on observations or evidence from some members of that category.

Existential Instantiation

A logical rule inferring the existence of at least one instance of a predicate; used in proofs to show something exists.

Universal Instantiation

A principle in logic that allows for the deducing of a statement about a specific instance from a general statement that applies to all instances.