This hyperbola is centered at the origin. Find its equation.

Foci: (-4,0) and (4,0)

Vertices: (-3,0) and (3,0)

The equation is ( x² / 9 ) - ( y² / 7 ) = 1

Step-by-step explanation:

Given the data in question;

hyperbola is centered at the  origin, this means h and k are all equals to 0.

Vertices: (-3,0) and (3,0)

Since y-coordinates are constant, this implies it is a hyperbola with horizontal transverse axis.

h - a = -3

0 - a = -3

a = 3

Foci: (-4,0) and (4,0)

h - c = -4

0 - c = -4

c = 4

we know that, for a hyperbola

c² = a² + b²

so

⇒ ( 4 )² = ( 3 )² + b²

16 = 9 + b²

b² = 16 - 9

b² = 7

So the equation for the hyperbola will be;

⇒ ( (x-h)² / a² ) - ( (y-k)² / b² ) = 1

so we substitute

⇒ ( (x-0)² / 3² ) - ( (y-0)² / 7 ) = 1

⇒ ( x² / 3² ) - ( y² / 7 ) = 1

⇒ ( x² / 9 ) - ( y² / 7 ) = 1

Therefore, The equation is ( x² / 9 ) - ( y² / 7 ) = 1

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i hope this answer !

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