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/![(-1)\cdot a = -a](https://tex.z-dn.net/?f=%28-1%29%5Ccdot%20a%20%3D%20-a)
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
.