Q7 of 70 Page 262

In each of the, find the equations of the hyperbola satisfying the given conditions.

Vertices ( 2, 0), foci ( 3, 0)

Vertices ( 2, 0), foci ( 3, 0)


Here, the vertices are on the x-axis.


Thus,


The equation of the hyperbola is of the form


Since, the vertices are (2,0), a = 2


Since, the foci are (3, 0), c= 3


We know that, a2 + b2 = c2


Thus, 22 + b2 = 32


⇒ b2 = 9 – 4 = 5


Hence, the equation of the hyperbola is


More from this chapter

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5

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

5y2 – 9x2 = 36

 6

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

49y2 – 16x2 = 784.

 8

In each of the, find the equations of the hyperbola satisfying the given conditions.

Vertices (0, 5), foci (0, 8)

 9

In each of the, find the equations of the hyperbola satisfying the given conditions.

Vertices (0, 3), foci (0, 5)