x = a cos t
y = b sin t
更新1:
Please provide the proof anyway if you think it is simple to prove graphically.
Ellipse
2009-08-22 7:23 pm
How to prove graphically that the equation of ellipse is:
x = a cos t
y = b sin t
x = a cos t
y = b sin t
回答 (3)
2009-08-23 2:34 am
✔ 最佳答案
In fact, the standard form of equation of an ellipse is:x2/a2 + y2/b2 = 1, where a and b are any real numbers with a and b =/= 0
Put x = acost and y = bsint into L.H.S.
Therefore,
L.H.S.
= (acost)2/a2 + (bsint)2/b2
= a2cos2t/a2 + b2sin2t/b2
= cos2t + sin2t
= 1
= R.H.S.
So, we finished the proof.
參考: Physics king
2009-08-23 12:36 am
Graphs do not provide any rigorous proof in mathematics.
2009-08-22 10:20 pm
Graphically? It won't be a proof!
收錄日期: 2021-04-19 15:12:24
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