The center of a hyperbola is located at the origin. one focus is located at (−50, 0) and its associated directrix is represented by the line x= 2.304/50. what is the equation of the hyperbola?

The equation of the hyperbola is :

The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)

As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin:

The distance from center to focus is 'c' and here focus is at (-50,0)

So, c= 50

Now if the distance from center to the directrix line is 'd', then

Here the directrix line is given as : x= 2304/50

Thus,

⇒

⇒ a² = 2304

⇒ a = √2304 = 48

For hyperbola, b² = c² - a²

⇒ b² = 50² - 48² (By plugging c=50 and a = 48)

⇒ b² = 2500 - 2304

⇒ b² = 196

⇒ b = √196 = 14

So, the equation of the hyperbola is :

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

answer: d. $20

step-by-step explanation:

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