Answer:
The standard form of this hyperbola is .
Step-by-step explanation:
From Analytical Geometry, the standard form of the hyperbola is defined by the following expression:
(1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Semiaxis lengths, dimensionless.
- Coordinates of the center, dimensionless.
Let the hyperbola be defined by , we proceed to derive the standard form by algebraic means:
1) Given
2) Commutative and associative properties/
3) Modulative, distributive and associative properties//Existence of the additive inverse
4) Perfect trinomial square//Commutative property
5) Distributive property//Definition of addition and subtraction.
6) /Compatibility with addition/Existence of additive inverse/Modulative property.
7) Compatibility with multiplication/Definition of division/Distributive property/Result.
The standard form of this hyperbola is .