Linear equation problem: solve the linear equation parallel to the point a (x0, Y0) and the line ax + by + C = 0

Linear equation problem: solve the linear equation parallel to the point a (x0, Y0) and the line ax + by + C = 0

If the line is parallel to the line ax + by + C = 0, then their slopes are equal, so k = - A / B, so the linear equation is y-y0 = - A / b (x-x0), which can be simplified

Prove: the linear equation passing through A0 (x0, Y0) and perpendicular to vector n = (a, b) is ax + by = ax0 + by0

It is proved that: let the point P coordinate on the line different from the point A0 (x0, Y0) be (x, y), then: vector a0p = (x-x0, y-y0) because the line a0p is perpendicular to the vector n = (a, b), that is, vector a0p ⊥ vector n, so: vector a0p · vector n = 0, that is, a (x-x0) + B (y-y0) = 0ax-ax0 + by-by0 = 0, so: ax + by = ax0 + by0 is easy to