 Hi, and welcome to the session. Let us discuss the following question. Welcome to the session. Let us discuss the following question. The question says, find the equation of the line which is equidistant from parallel lines 9x plus 6y minus 7 is equal to 0 and 3x plus 2y plus 6 is equal to 0. Let's now begin with the solution. Given parallel lines are 9x plus 6y minus 7 is equal to 0 and 3x plus 2y plus 6 is equal to 0. On multiplying this equation by 3, we get 9x plus 6y plus 18 is equal to 0. Let's name this equation as equation number 1 and this as 2. We know that equation of parallel lines only differ by a constant. If ax plus by plus c is equal to 0 is an equation of line, then line parallel to this line will have equation ax plus by plus d is equal to 0. So let the equation of third line which is parallel to line 1 and 2x5 plus c is equal to 0. Let's name this equation as equation number 3. In the question it is given that line 3 is equidistant from line 1 and line 2. This means the distance between line 1 and line 3 and distance between line 2 and line 3 is same. So let's first find the distance between line 1 and 3. We know that distance between two parallel lines whose equations are ax plus by plus c is equal to 0 and ax plus by plus d is equal to 0 is given by mod of c minus d upon square root of a square plus b square. Now here c is equal to minus 7 and d is equal to c and a is equal to 9 and b is equal to 6. So distance between line 1 and line 3 is mod of minus 7 minus c upon square root of 9 square plus 6 square. Now we will find distance between line 2 and 3. Distance between line 2 and line 3 is mod of c minus 18 upon square root of 9 square plus 6 square. Now the distance between line 1 and line 3 is same as distance between line 2 and line 3. So mod of minus 7 minus c upon square root of 9 square plus 6 square is equal to mod of c minus 18 upon square root of 9 square plus 6 square. This implies minus 7 minus c is equal to c minus 18. This implies minus 2 c is equal to minus 11 and this implies c is equal to 11 by 2. So the required equation of line is xy plus 11 by 2 is equal to 0 or we can say that 18x plus 12y plus 11 is equal to 0. This is our required answer. So this completes the section. Bye and take care.