Question

which statements are true for a hyperbola that has vertices at (-3,-3) and (5,-3) and a conjugate axis 6 units long

Answer 1

Given :   hyperbola that has vertices at (-3,-3) and (5,-3) and a conjugate axis 6 units

To Find :  hyperbola

Solution:

Vertices are (-3 , - 3)  & ( 5 , - 3)

(-3 + 5)/2 =  1  

5 -(-3) = 8

transverse axis =  8

2a = 8

=> a = 4

conjugate axis 6

=> 2b = 6

=> b = 3

( x - 1)² / a²   -  ( y + 3)²/b² = 1

( x - 1)² / 4²   -  ( y + 3)²/3² = 1

Center = (-1 , - 3)

Hyperbola opens  Horizontally  

c² = a² + b²

=> c = 5

Learn More:

अतिपरवलय  rac{x^{2}}{a^{2}}

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