Question

1.AB是圆O的直径且│AB│=2a,M为圆上一动点,作MN⊥AB,垂足为N,在OM上取一点P,使│OP│=│MN│,求

Answer 1

圆半径为a设M坐标为(acosθ,asinθ)则|MN|=|asinθ|P在OM上,设P坐标为(rcosθ,rsinθ),其中r>0所以r=|asinθ|P坐标为(|asinθ|cosθ,|asinθ|sinθ)将P坐标记为(x,y),则我们有x2+y2=a2*(sinθ)2所以(x2+y2)2 = (ay)2(x2+y2-ay)(x2+y2+ay)=0