（1）c=2,设椭圆方程为x^2/(b^2+4)+y^2/b^2=1,把点P的坐标代入得25/(b^2+4)+9/b^2=4,去分母得25b^2+9b^2+36=4b^4+16b^2,4b^4-18b^2-36=0,2b^4-9b^2-18=0,b^2=6,(舍去负值）所求椭圆方程为x^2/10+y^2/6=1.请检查第二...AB为直径的圆..谢谢帮助设AB:y=x+m,代入椭圆方程得3x^2+5(x^2+2mx+m^2)=30,8x^2+10mx+5m^2-30=0,设A(x1,y1),B(x2,y2),则x1+x2=-5m/4,x1x2=(5m^2-30)/8.以AB为直径的圆恰好过椭圆C的中心O(0,0),∴OA*OB=x1x2+y1y2=x1x2+(x1+m)(x2+m)=2x1x2+m(x1+x2)+m^2=(5m^2-30-5m^2)/4+m^2=0,∴m=土√30/2，∴直线L的方程为y=x土√30/2.