PPT Slide

Solution to #6: The Algebra
Given: s1 + s2 = k

(f - x)2 + y2 = s12 … (eq. i)

(f + x)2 + y2 = s22 … (eq. ii)

1.) Let (x,y) = (a,o). This gives k = 2a, and

s1 = 2a - s2

2.) Let (x,y) = (0,b). This gives s1 = s2 = (f2+b2)1/2, and f2 = a2 - b2

3.) Result 2.) ? eq. ii gives

s2 = a + (x/a)(a2 - b2)1/2

4.) Result 2.) and 3.) ? eq. ii gives

(x/a)2 + (y/b)2 = 1

Be careful: The algebra gets messy!

From geometry:

Previous slide

Next slide

Back to first slide

View graphic version