Question

5 The eccentricity of a hyperbola is defined as e Find an equation of a hyperbola with vertices (3 - 3) and (-1, -3) and e- The equation of the hyperbola is (Type an equation. Type your answer in standard form)

Answer 1

a 2 Note that it the equation of the hyperbola.is (n-1)2 (y-k12 E1 62 then (hk) be the centre of hyperbola. The axis of hyperbola must be parallel to n-axis so Co-ordinate y = Constant =k

Here c = the distance of focus of the hyperbola from centre chok), c2=a2 +62 c. a So the encetricity of hyperbola V a2 +62 a, Here a= distance between two vertices 2

here the vertex/ vertices are 13,-3) and (-1,-3) So, y=-3 = Constant So, The axis of hyperbola must be parallel to the x-axis. 1 2 it 3 f --- 1 -1 -2 So the distance between two vertices is 4 unit, (1-3) So, a= 4/ (-1,-3) 13,-3). 2 (22+62) 02 here ra2+62 5 2 25 (Square both side) 2542- 4027462 # 462=2102 + 462 = 2184 [a2-4 from 0] 62=21. In the figure the middle point between two vertex /vertices is (1,-3) so the centre is (hk)=(1-3) So the equation of the hyperbola is (n-1)2 (y- k2 az 62 = 1 A (n-1)2 19+3)2 -1 4 21
At the end check out the box.... Equation number (A) is the equation of the hyperbola