How to find the coordinates of a point on a line?

Question

Mathematics

There are 2 points P1(x1,y1),P2(x2,y2) that define a line.
1 question) How to find the function of a line in the format ax + by +c = 0 based on the values ​​of the coordinates of the points P1 and P2?
Question 2) If there is, on a straight line, a point M(x,y), knowing the length of the segment (P1M = L) and the value of the coordinates of the points P1 and P2, how can you find out the value of the coordinates of the point M?

Answer 1

1 question. (x-x1)/(x2-x1) = (y-y1)/(y2-y1) separate cases when 0 in the denominator (google the equation of a straight line for 2 points)
2 question: find the lengths of P2M and P1P2 and google "point coordinates dividing the segment in relation to "