Q. 55.0( 2 Votes )

# Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of 45^{0} to the lines 3x + y – 5 = 0.

Answer :

__Given:__ equation passes through (2,3) and make an angle of 45^{0}with the line 3x + y – 5 = 0.

__To find:__ equation of given line

Explanation:

We know that the equations of two lines passing through a point x1,y1 and making an angle α with the given line y = mx + c are

Here,

Equation of the given line is,

3x + y – 5 = 0

⇒ y = - 3x + 5

Comparing this equation with y = mx + c we get, m = - 3

x_{1} = 2, y_{1} = 3, α = 45∘, m = - 3.

So, the equations of the required lines are

⇒ x + 2y – 8 = 0 and 2x – y – 1 = 0

Hence, Equation of given line is x + 2y – 8 = 0 and 2x – y – 1 = 0

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