The linear y equals 2x minus 6 and the inverse proportional function y equals K parts of X (x is greater than 0) of the image intersection at point a (4,2), and X axis intersection at point B 1. Find the value of K and the coordinates of point B 2. Whether there is a point C on the X axis, so that the triangle ABC is isosceles triangle, if there is, find the coordinates of point C, if not, please explain the reason

The linear y equals 2x minus 6 and the inverse proportional function y equals K parts of X (x is greater than 0) of the image intersection at point a (4,2), and X axis intersection at point B 1. Find the value of K and the coordinates of point B 2. Whether there is a point C on the X axis, so that the triangle ABC is isosceles triangle, if there is, find the coordinates of point C, if not, please explain the reason

1. Point a (4,2) is substituted by y = K / X to get: 2 = K / 4, so k = 8b (x, 0) is substituted by y = 2x-6 to get: 0 = 2x-6, so x = 3, B coordinates are: (3,0) 2. To become an isosceles triangle, there are two cases. (1) AB = BC, because AB = radical (1 ^ 2 + 2 ^ 2) = radical 5, so as long as the distance between point C and B is radical 5, that is, C