椭圆x^2/a^2+y^2/b^2=1的面积S=πab
方程 ax^2+bxy+cy^2=d如果b0,要化成标准式的话需用到旋转变换,设
x=Xcost+Ysint
y=-Xsint+Ycost
代入：ax^2+bxy+cy^2=d
得：a(X^2cos^2t+Y^2sin^2t +XYsin2t)+b[-X^2 sintcost+Y^2sintcost+XYcos2t]+c(X^2sin^2t+Y^2cos^2t-2XYsintcost)=d
即：X^2[acos^2 t-bsintcost+csin^2t]+XY[asin2t+bcos2t-csin2t]
+Y^2[asin^2 t+bsintcost+ccos^2 t]=d
由XY项的系数为0,得：asin2t+bcos2t-csin2t=0--> tg2t=b/(c-a)
由此求得t,进而消去了XY项,就化为了标准式了.