粉末t-7柔软焦点什么意思

粉末t-7柔软焦点什么意思

1.椭圆e:x^2/2+y^2=1的右焦点是F(1,0),∴抛物线q的方程是y^2=4x.①2.抛物线q的准线l:x=-1与x轴交于点D(-1，0),设l上的动点P为(-1,p),PF的斜率=-p/2,PF:y=(-p/2)(x-1),②即x=1-2y/p,代入①，y^2+8y/p-4=0,△=64/p^2+16,|AB|=√[△（1+4/p^2)],D到PF的距离h=2/√(1+4/p^2),∴S△ABD=(1/2)|AB|h=√(64/p^2+16),它的取值范围是(4,+∞).3.把②代入椭圆方程得x^2/2+(p^2/4)(x^2-2x+1)=1,整理得(2+p^2)x^2-2p^2x+p^2-4=0,设M(x1,y1),N(x2,y2),则x1+x2=2p^2/(2+p^2),x1x2=(p^2-4)/(2+p^2),由②，y1y2=(p^2/4)(x1-1)(x2-1)=(p^2/4)x1x2-(p^2/4)(x1+x2)+p^2/4,以MN为直径的圆过点D,DM⊥DN,(x1+1)(x2+1)+y1y2=0,(1+p^2/4)x1x2+(1-p^2/4)(x1+x2)+1+p^2/4=0,(4+p^2)(p^2-4)+2p^2(4-p^2)+(4+p^2)(2+p^2)=0,p^4-16-2p^2+8p^2+p^4+6p^2+8=14p^2-8=0,p^2=4/7,p=土2√7/7，∴P(-1，土2√7/7).