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Question
Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x-axis.
Solution
The equation of the line parallel to the x-axis is y = b.
It is given that y = b passes through (4, 3).
∴ 3 = b
\[\Rightarrow\] b = 3
Thus, the equation of the line parallel to the x-axis and passing through (4, 3) is y = 3.
Similarly, the equation of the line perpendicular to the x-axis is x = a.
It is given that x = a passes through (4, 3).
∴ 4 = a
\[\Rightarrow\] a = 4
Thus, the equation of the line perpendicular to the x-axis and passing through (4, 3) is x = 4.
Hence, the required lines are x = 4 and y = 3.
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