Find the equation of the hyperbola satisfying the give conditions: Vertices (±2,0) foci (±3,0)
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Solution
Vertices (±2,0) foci (±3,0) Clearly the vertices are on the x-axis. Therefore, the equation of the hyperbola is of the form x2a2−y2b2=1 Since the vertices are (±2,0)
⇒a=2 and foci are (±3,o)⇒ae=3 We know that b2=a2(e2−1)=a2e2−a2=9−4=5 Thus the equation of the hyperbola is x24−y25=1