The joint equation of a pair of lines passing through point (1,4) , one of which is parallel to X-axis and the other makes an angle of 45^ with the positive direction of X-axis, is

Step-by-step solution

The first line passes through (1,4) and is parallel to the X-axis. Its slope is m₁ = 0 . Equation of the first line is y - 4 = 0 . The second line passes through (1,4) and makes an angle of 45^ with the positive direction of the X-axis. Its slope is m₂ = 45^ = 1 . Equation of the second line is y - 4 = 1(x - 1) x - y + 3 = 0 . The joint equation of the pair of lines is the product of their individual equations: (y - 4)(x - y + 3) = 0 Expanding the product, we get: xy - y^2 + 3y - 4x + 4y - 12 = 0 Simplifying the te