Ex 11.4, 7 - Chapter 11 Class 11 Conic Sections

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Ex 11.4, 7 Find the equation of the hyperbola satisfying the given conditions: Vertices ( 2, 0), foci ( 3, 0) Vertices are ( 2, 0) Hence, vertices are on the x-axis Equation of hyperbola is of the form x2 a2 y2 b2 = 1 Now, Co-ordinate of vertices = ( a,0) & Vertices = ( 2,0) ( a, 0) = ( 2, 0) Hence a = 2 Also, given coordinates of foci = ( 3, 0) And we know that co-ordinates of foci are ( c, 0) ( c, 0) = ( 3, 0) c = 3 Also c2 = a2 + b2 Putting a = 2, c = 3 32 = 22 + b2 9 = 4 + b2 5 = b2 b2 = 5 Thus, Equation of hyperbola 2 2 2 2 = 1 2 2 2 2 5 = 1 = 1