The standard equation of an ellipse w/center (0,0) Vertices(0,+-a) and foci (0,+-c) is.......

Question

x^2/b^2+y^2/a^2=1 where b^2=a^2-c^2. The eccentricity of an ellipse,denoted by e is defined as follows.

e=distance between foci/distance between the vertices =2c/2a=c/a

Find the eccentricity of an ellipse x^2/7 +y^2/16 =1

Answer 1

Eccentricity of an ellipse describe the shape of an ellipse, tells you if an ellipse is circular or it has an oval shape. 0<e<1. If e ≈ 0 the ellipse will appear to be circular. If e=0 we have a circle, if e ≈1 the ellipse will have an oval shape.

In you case: x^2/7 +y^2/16 =1 (x^2/b^2+y^2/a^2=1) you have a=4 and b=sqrt{7} therefore c^2=a^2-b^2=16-7=9 therefore c=3

You can now calculate e=c/a=3/4=0.75.