Question

if a,b,c are in a A.P., then prove that the straight line ax+by+c=0 will always pass through the point(-1,2)

Answer 1

If a, b, c are in A. P then 2b=a+c
ax+by+c=0 implies ax+by+2b-a=0
a(x-1)+b(y+2)=0
(x-1)+b/a(y+2)=0 represents a set of lines passing through the point of intersection of x-1=0 and y+2=0
Therefore the point of intersection is (1,-2)