橢圓中心在原點(diǎn)吧.
這樣的話,2個(gè)焦點(diǎn)坐標(biāo)分別為A(1,0)和B(-1,0).
點(diǎn)C(2,1)在橢圓上.
橢圓的2個(gè)焦點(diǎn)到點(diǎn)C的距離和d=(1^2+1^2)^(1/2) + (3^2+1^2)^(1/2)=2^(1/2)+(10)^(1/2).
X軸上橢圓的半軸長(zhǎng)=d/2.(d/2)^2 = 3+5^(1/2)
Y軸上橢圓的半軸長(zhǎng)=[(d/2)^2 - 焦距的平方]^(1/2)={[3+5^(1/2)]-1]^(1/2)={2+5^(1/2)}^(1/2).
橢圓方程為
X^2/[3+5^(1/2)] + Y^2/[2+5^(1/2)] = 1