Page 11 - Jose Garcia_2013150017_grade12 ebook

Both sides squared get:

2
√( + ) + 0 2 = 2
0

2
2
−√( − ) +
0
0
If Both sides squared get:

2
2
2
2
2
→ ( + ) + 0 2 = 4 − 4 √( − ) + 0 2 + ( − ) +
0
0
0
0
2
2
2
2
→ 0 2 + 2 + + 0 2 = 4 − 4 √( − ) + 0 2 + 0 2 − 2 +
0
0
0
2
2
→ 4 √( − ) + 0 2 = 4 − 4
0
0
2
2
→ √( − ) + 0 2 = ( − )
0
0
Both sides squared get:
2
2
2
2
→ ( − ) + 0 2 = ( − )
0
0
2
2
2
4
2
2
2 2
2
→ 0 2 − 2 + + 0 2 = − 2 +
0
0
0
2
2
2
2
2
2
2
→ ( − ) 0 + 0 2 = ( − )
If both sides are divided by ( − ) we get :
2
2
2
0 2 0 2
2
2
2 + ( − ) = 1
2
2
2
on the ellipse there is a provision that − = , so the above equation becomes
2 2
+ = 1
2 2
Pay attention to the equation and the image of the ellipse above so that it can be
concluded some of these things.
1. Its center is point O(0,0).
2. The focus is the points F1(−c,0) and F2(c,0)
3. The x-axis is the major axis and and the y-axis is the minor axis if a > b.
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