Q17 of 70 Page 255

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Foci ( 3, 0), a = 4

Foci = (), a=4


Since the foci are on the x-axis, the major axis is along the x-axis.


Therefore, the equation of the ellipse will be of the form =1, where a is the semi-major axis.


Accordingly, c = 3 and a=4.


It is known that a2 = b2+c2.


a2 = 82+62 = 64+36 =100


16 = b2 + 9


b2 = 16 – 9 = 7


Thus, the equation of the ellipse is = 1.


More from this chapter

All 70 →
15

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Length of major axis 26, foci ( 5, 0)

 16

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Length of minor axis 16, foci (0, 6).

 18

In each of the following, find the equation for the ellipse that satisfies the given conditions:

b = 3, c = 4, centre at the origin; foci on the x axis.

 19

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).