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If the focus of a hyperbola is ( ± 3,0 ) and the equation of a tangent is 2 x + y - 4 = 0 , then the equation of the hyperbola is

Options

  1. A4 x 2 - 5 y 2 = 20
  2. B5 x 2 - 4 y 2 = 20
  3. C4 x 2 - 5 y 2 = 1
  4. D5 x 2 - 4 y 2 = 1

Correct answer

A. 4 x 2 - 5 y 2 = 20

Step-by-step solution

Given, ± a e ,   0 = ± 3 ,   0 ⇒     a e = 3 ⇒   a 2 e 2 = 9   ⇒   b 2 + a 2 = 9 ...(i) ∵   2 x + y - 4 = 0 ⇒       y = - 2 x + 4 is the tangent to the hyperbola ∴     4 2 = a 2 - 2 2 - b 2   ∵ c 2 = a 2 m 2 - b 2 ⇒     4 a 2 - b 2 = 16 ...(ii) On solving Eqs. (i) and (ii), we get, a 2 = 5 ,   b 2 = 4   ∴ Equation of hyperbola is x 2 5 – y 2 4   = 1 &#8

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