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EXPLANATION.

Equation of the hyperbola,

⇒ Vertices = (±2,0).

⇒ Foci = (±3,0).

As we know that,

General equation of hyperbola,

⇒ x²/a² - y²/b² = 1.

Vertices of the hyperbola = (±a,0).

Foci of the hyperbola = (±c,0).

⇒ a = 2.

Squaring on the both sides, we get.

⇒ a² = 4.

⇒ c = 3.

Squaring on both sides, we get.

⇒ c² = 9.

As we know that,

⇒ c² = a² + b².

⇒ 9 = 4 + b².

⇒ 9 - 4 = b².

⇒ 5 = b².

⇒ Equation = x²/4 - y²/5 = 1.

MORE INFORMATION.

Equation of the normal.

(1) = The equation of normal to the hyperbola x²/a² - y²/b² = 1 at (x₁, y₁) is a²x/x₁ + b²y/y₁ = a² + b² = a²e².

(2) = The equation of normal at (a sec∅, b tan∅) to the hyperbola x²/a² - y²/b² = 1 at ax cos∅ + by cot∅ = a² + b².

(3) = Slope form : y = mx - m(a² + b²)/√a² - b²m².

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