1.假設橢圓之長軸平行於x軸或y軸,且滿足下列條件,求其方程式:
(1)中心和原點重合,y軸為長軸,正焦弦長是2,二焦點距離2√ 2
(2)焦點為(-1,1),(7,1),長軸之二端點為(-2,1),(8,1)
(2)焦點為(-1,1),(7,1),長軸之二端點(-2,1),(8,1)
(3)長軸方程式x=5,短軸方程式y=1,短軸為長軸之3/5倍,且中心到焦點之距離為12
(4)中心為(1,2),二焦點間之距離為6,長軸長為8
(5)以中心為原點,軸為座標軸,通過(2,3),(-1,4)二點
(6)中心為(1,2),長軸平行於x軸,且長軸長為短軸長之3倍,且通過(4,3)
(7)若一橢圓的中心為(6,-3),軸平行座標軸,且通過二點(4,1),(3,-2),求此橢圓方程式
(8)過(3,2),且與x^2/9+y^2/4=1共焦點1.
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