wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find what straight lines are represented by the following equation and determine the angles between them.
x2+2xysecθ+y2=0

Open in App
Solution

x2+2xysecθ+y2=0

Applying quadratic formula by assuming y as variable

y=b±b24ac2a

here a=1,b=2xsecθ,c=x2

y=2xsecθ±4x2sec2θ4(1)(x2)2y=2xsecθ±2xsec2θ12y=xsecθ±xtanθy=xsecθ+xtanθ,y=xsecθxtanθ.......(i)y=xcosθ±xsinθcosθy=xcosθ+xsinθcosθ,y=xcosθxsinθcosθ(1sinθ)x+cosθy=0,(1+sinθ)x+cosθy=0

So the eqaution of lines are (1sinθ)x+cosθy=0 and (1+sinθ)x+cosθy=0

From (i)

Slope of first line m1=secθ+tanθ

Slope of second line m2=secθtanθ

Angle between two straight lines that is tanα=m1m21+m1m2=(secθ+tanθ)(secθtanθ)1+(secθ+tanθ)(secθtanθ)

tanα=secθ+tanθ+secθ+tanθ1(tanθsecθ)(tanθ+secθ)=2tanθ1(tan2θsec2θ)tanα=2tanθ1(1)=tanθα=tan1(tanθ)=θ


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Tango With Straight Lines !!
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon