1)
由图知CA-CB=CD-DB=√5+2-(√5-2)=4=2a -->a=2,c=√5,b=1
所以点C的轨迹为双曲线且为其右支:x²/4 - y²/1 = 1 (x>=2)
2)
设MP直线为x=my+2,∵向量MP·向量MQ=0 ∴MP⊥MQ
则MQ直线为x=-y/m +2
将MP MQ代入双曲线方程中解得P((2m²-8)/(4-m²),4m/(4-m²)) ,
Q((2-8m²)/(4m²-1),(4m²+m)/(4m²-1))
由此可解得PQ直线,有点繁.之后再确定M是否在PQ直线上.