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

The base BC (=2a) of a triangle ABC is fixed; the axes being BC and a perpendicular to it through its middle point, find the locus of the vertex A, when the product of the tangents of the base angles is given (=λ).

Open in App
Solution

Let O be the mid point of base BC of triangle ABC and the vertex A be (h,k)

In ABDtanx=kh+a....(i)

In ACDtanϕ=kha.....(ii)

ϕ+y=πy=πϕ

Given tanxtany=λ

tanxtan(πϕ)=λtanx(tanϕ)=λtanxtanϕ=λ

substituting (i) and (ii)

kh+a×kha=λk2h2a2=λk2=λh2+a2λk2+λh2=a2λ

Replacing h by x and y by k

y2+λx2=a2λ

is the required locus of vertex A


695691_640690_ans_7dc28f77f0964999a757105a81add788.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle and Its Measurement
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon