The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)

Step-by-step solution

Let the equation of the line be x a + y b = 1 , where a and b are the non-zero intercepts on the x-axis and y-axis respectively. Given that the sum of the non-zero intercepts is zero, we have: a + b = 0 b = -a Substituting b = -a into the equation of the line, we get: x a + y -a = 1 x - y = a Since the line passes through the point A(3, 4) , we substitute x = 3 and y = 4 into the equation: 3 - 4 = a a = -1 Since a = -1 0 , this is a valid non-zero intercept. The corresponding value of b is b = -(-1) = 1 . Thus, the