Question

关于直线与圆的关系若点P在直线 y=-x 上,过点P作圆（x-a）^2 - （y-2*a)^2 = a^2 的切线PTT

Answer 1

设P坐标(m,-m),圆O圆心坐标O(a,2a)

|OP|^2=(m-a)^2+(-m-2a)^2=2m^2+5a^2+2ma

|OT|^2=a^2

|PT|^2=|OP|^2-|OT|^2=2m^2+2ma+4a^2=2(m+a/2)^2+3.5a^2

所以当m=-a/2时,|PT|有最小值,即是:根号(3.5a^2)=根号7/2*|a|

选择:B