Let origin be the centre, ± 3 , 0 be the foci and 3 2 be the eccentricity of a hyperbola. Then the line 2 x - y - 1 = 0

Step-by-step solution

Given, Origin be the centre, ± 3 , 0 be the foci and 3 2 be the eccentricity of a hyperbola, Now we know that foci is ± a e , 0 ≡ ± 3 , 0 , So a e = 3 and given e = 3 2 then a = 1 2 , Now by formula b 2 = a 2 e 2 - 1 we get b = 5 4 So, equation of hyperbola will be x 2 1 4 - y 2 5 16 = 1 ⇒ 20 x 2 - y 2 = 80 Now putting the value of y from the line 2 x - y - 1 = 0 in hyperbola to check intersecting or not, So, 20 x 2 - 2 x - 1 2 = 80 ⇒ 16 x 2 + 4 x - 81 = 0 Now discriminant D = 4 2 +