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Question

Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of 45 to the line 3x+y5=0

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Solution

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

yy1=m±tan α1±m tan α(xx1)

Here,

Equation of the given line is,

3x+y5=0

y=3x+5

Comparing this equation with y=mx+c

we get,

m = -3

x1=2, y1=3, α=45, m=3

So, the equations of the required lines are

y3=3+tan 451+3 tan 45(x2) and y3

=3tan 4513 tan 45(x2)

y3=3+11+3(x2) and y3=3113(x2)

y3=12(x2) and y3=2(x2)

x+2y8=0 and 2xy1=0

y3=3+tan 451+3 tan 45(x2) and y3=3tan 4513 tan 45(x2)


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