Question

7. Vertices (+ 2, 0), foci (+ 3, 0)

Answer 1

The given coordinates of vertices are ( ±2,0 ) and coordinates of foci are ( ±3,0 ) .

Since the vertices are on the x axis, the equation of the hyperbola is represented as,

x 2 a 2 − y 2 b 2 =1 , where x is the transverse axis.(1)

Since x axis is the transverse axis, coordinates of Foci = (±c,0)

∴c=3

Since x axis is the transverse axis, coordinates of vertices = (±a,0)

∴a=2

Now: a 2 + b 2 = c 2 2 2 + b 2 = 3 2 b 2 =9−4 b= 5

Substitute the values of a and b in equation (1)

x 2 4 − y 2 5 =1

Thus, the equation of hyperbola with vertices (±2,0) and foci ( ±3,0 ) is x 2 4 − y 2 5 =1 .