Answer:
Equation is y²/36 - x²/64 = 1 ....
Step-by-step explanation:
It is given that vertices are (0, ±6) that makes this a vertical aligned hyperbola.The center of the hyperbola is midway between the left and right vertex which makes the center equal to (0,0).The general equation of vertical hyperbola is:
y²/a² - x²/b² = 1
where a is the distance between the vertex and the center,which is equal to a=6.The equation for the asymptotes of a vertical aligned hyperbola is:
y = +/- a/b x
It is given that:
a/b = 3/4
6/b = 3/4
By cross multiplication:
6*4 = 3*b
24= 3b
Divide both sides by 3
24/3 = 3b/3
b = 8
The formula for this vertically aligned hyperbola is:
y²/36 - x²/64 = 1
Equation is y²/36 - x²/64 = 1 ....
