The acute angle between the line 4 x-2 y+13=0 and the line which makes equal intercepts with the co-ordinate axes is

Step-by-step solution

To determine the acute angle between the lines, begin by finding their slopes. The first line, 4x - 2y + 13 = 0 , can be rearranged to slope-intercept form: 2y = 4x + 13 , yielding y = 2x + 13 2 , so m₁ = 2 . The second line makes equal intercepts on the axes. For intercept a , its equation is x + y = a , or in slope-intercept form, y = -x + a , so m₂ = -1 . The acute angle between lines with slopes m₁ and m₂ is given by = | m₁ - m₂ 1 + m₁ m₂ | . Substituting m₁ = 2 and m₂ = -1 , compute = | 2 + 1 1 - 2 | = | 3 -1