Q. 54.8( 5 Votes )

# Find the equations of the straight lines which pass through (4, 3) and are respectively parallel and perpendicular to the x–axis.

Given, A line which is perpendicular and parallel to x–axis respectively and passing through (4, 3)

To Find: Find the equation of that line.

Formula used: The equation of line is [y – y1 = m(x – x1)]

Explanation:

Case 1 : When Line is parallel to x–axis

So, The parallel lines have equal slopes,

And, the slope of x–axis is always 0, then

The slope of line, m = 0

Coordinates of line are (x1, y1) = (4, 3)

The equation of line is y – y1 = m(x – x1) – – – – (1)

By putting the values in equation (1), we get

y – (3) = 0(x – 4)

y – 3 = 0

Case 2: when line is perpendicular to x–axis

Here, The line is perpendicular to the x–axis, then x is 0 and y is – 1.

So, The slope of the line is, m =

m =

Coordinates of line are (x1, y1) = (4, 3)

The equation of line = y – y1 = m(x – x1)

By putting the values, we get

x = 4

Hence, The equation of line when it is parallel to x –axis is y = 3 and it is perpendicular is x = 4.

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