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

If the curve y=ax and y=bx intersect at angle α then, tan α=

A
ab1+ab
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
logalogb1+logalogb
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
a+b1ab
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
loga+logb1logalogb
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B logalogb1+logalogb
If two lines with slope m1&m2 intersect such that θ is the angle between them, then
tanθ=m1m21+m1m2(1)

The two curves,
y=ax and y=bx (where ab)
Intersect for x=0 at (0,1)

Now,
Slope of the tangent at (0,1) to the curve y=ax is m1=ddxax](0,1)=logax](0,1)=loga
Slope of the tangent at (0,1) to the curve y=bx is m2=ddxbx](0,1)=logbbx]0,1=logb
the angle between them is obtained using (1)
tanα=logalogb1+log.logb

Hence, this is the answer.

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