Respuesta :
Answer:
h= -3
k= 1
a= 3
b= 2
Center: (-3, 1)
Slope of Asymptote: 2/3
Step-by-step explanation:
Edge
The standard form of the provided equation is (x+3)²/9 - (y - 1)²/4 = 1 and h = -3, k = 1, a = 3, and b = 2.
What is hyperbola?
It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have an equation:
4x² - 9y² + 24x + 18y - 9 = 0
4x² + 24x - 9y² + 18y - 9 = 0
4(x² + 6x) - 9(y² - 2y) - 9 = 0
4[(x+3)² - 9] - 9[(y - 1)² - 1] - 9 = 0
4(x+3)² - 36 - 9(y - 1)² + 9 - 9 = 0
4(x+3)² - 9(y - 1)² = 36
4(x+3)²/36 - 9(y - 1)²/36 = 1
(x+3)²/9 - (y - 1)²/4 = 1
From the above equation:
h = -3
k = 1
a = 3
b = 2
Center: (-3, 1)
The slope of Asymptote: 2/3
Thus, the standard form of the provided equation is (x+3)²/9 - (y - 1)²/4 = 1 and h = -3, k = 1, a = 3, and b = 2.
Learn more about the hyperbola here:
brainly.com/question/12919612
#SPJ2
