Plz
which is the equation of a hyperbola with directrices at x = ±2 and foci at (4, 0) and (−4, 0)?
x squared over 8 minus y squared over 8 equals 1
x squared over 8 minus y squared over 16 equals 1
y squared over 8 minus x squared over 8 equals 1
y squared over 16 minus x squared over 8 equals 1

Step-by-step explanation:

If the equation of the of the hyperbola is , then the eccentricity, and the directrices are and the foci are (± ae,0).

Now, given that ae = 4 and (1)

So,

⇒ a² = 8

⇒ a = 2√2 units.

Now, from equation (1) we get, ae = 4

⇒ e = √2 as a = 2√2

Now,

⇒

⇒ b² = 8

Hence, the equation of the hyperbola is (Answer)

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step-by-step explanation:

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