wiz-icon
MyQuestionIcon
MyQuestionIcon
306
You visited us 306 times! Enjoying our articles? Unlock Full Access!
Question

Equations of the lines through the point (3, 2) and making an angle of 45° with line x – 2y – 3 = 0 are __________.

Open in App
Solution

Let us suppose slope of line be m which makes an angle of 45āˆ˜ with x − 2y − 3 = 0

Slope of x-2y-3 =0 is 12 tan45°=m-121+m2i.e. 1=m-121+m2i.e. ±1+m2=m-12i.e. m2=32 or -1-m2=m-12i.e. m=3 or 3m2=-12 i.e. m=-13 y=3x+c is the equation of line or y=-13x+c
Since this line passes through (3, 2)
i.e. 2 = 9 + c
i.e. c = – 7
∴ Equation of line is y = 3x – 7
i.e. 3x – y – 7 = 0

or 2=-133+ci.e. c=3 y=-13x+3i.e. 3y+x-9=0
∴ Equations of lines are 3x – y – 7 = or x + 3y – 9 = 0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equation of Line perpendicular to a given Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon