Maths-Ecclipse

Question

What is the eccentricity of the ellipse 16x2 + 7y2 = 112.

Answer 1

Here is the definition of eccentricity:

http://www.mathopenref.com/ellipseeccentricity.html

 

You can see that we need to know where the 2 focus points are.

 

Here is the formula for the distance to the focus:

http://www.mathopenref.com/ellipsefoci.html

 

1.  find the two semi-axes of the ellipse:

for x = 0, y = +/- √16      (y^2 = 16)

for y = 0, x = +/- √7        (x^2 = 7)

so the focus distance F = √(16 - 7) = 3

 

2. Now find "a" in the eccentricity formula

a^2 = c^2 + b^2  (b is the "semi-minor axis" and--from step 1--is √7; c is the focus distance from step 1)

So a^2 = 3^2 + 7

a = 4

 

3.  Eccentricity = c/a = 3/4 = 0.75

 

draw a picture to help make it clear