If `aa^1= b b^1 != 0`, the points where the coordinate axes cut the lines `ax + by + c=0 and a^1 x + b^1 y+c^1=0` form

Prove that the line through the point (x_1,y_1) and parallel to the line Ax + By + C = 0 is A (x- x_1) + B (y- y_1) = 0

Prove that the line through the point (x_1,y_1) and parallel to the line Ax + By + C = 0 is A (x- x_1) + B (y -y_1) = 0.

If a , b , c are in G.P. write the area of the triangle formed by the line a x+b y+c=0 with the coordinates axes.

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b, c are consecutive odd integers then the line ax + by + c = 0 will pass through

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b, c are consecutive odd integers then the line ax + by + c = 0 will pass through

The algebraic sum of distances of the line ax + by + 2 = 0 from (1,2), (2,1) and (3,5) is zero and the lines bx - ay + 4 = 0 and 3x + 4y + 5=0 cut the coordinate axes at concyclic points. Then (a) a+b=-2/7 (b) area of triangle formed by the line ax+by+2=0 with coordinate axes is 14/5 (c) line ax+by+3=0 always passes through the point (-1,1) (d) max {a,b}=5/7

The algebraic sum of distances of the line ax + by + 2 = 0 from (1,2), (2,1) and (3,5) is zero and the lines bx - ay + 4 = 0 and 3x + 4y + 5=0 cut the coordinate axes at concyclic points. Then (a) a+b=-2/7 (b) area of triangle formed by the line ax+by+2=0 with coordinate axes is 14/5 (c) line ax+by+3=0 always passes through the point (-1,1) (d) max {a,b}=5/7

Prove that the line through the point (x_(1) , y_(1)) and parallel to the line Ax + By + C =0 " is " A (x - x_(1)) + B (y - y_(1)) = 0 .

Prove that the line through the point (x_(1) , y_(1)) and parallel to the line Ax + By + C =0 " is " A (x - x_(1)) + B (y - y_(1)) = 0 .

Prove that the line through the point (x_(1) , y_(1)) and parallel to the line Ax + By + C =0 " is " A (x - x_(1)) + B (y - y_(1)) = 0 .