CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let A(1,0) and B(2,0) be two points. A point M moves in the plane in such a way that MBA=2MAB. Then the point M moves along  


A
a straight line
loader
B
a parabola 
loader
C
an ellipse 
loader
D
a hyperbola
loader

Solution

The correct option is D a hyperbola
Let the coordinates of point M be (h,k) and MAB=θ

From MDA
tanθ=kh+1     ...(1)
Now, from MDB
tan2θ=k2h     ...(2) 

As we know,
tan2θ=2tanθ1tan2θ

From (1) and (2),
k2h=2 .kh+11(kh+1)2

k2h=2k(h+1)h2+1+2hk2

h2+1+2hk2=2h2h2+4

3h2k2=3

h21k23=1 which represents a hyperbola.

Mathematics

Suggest Corrections
thumbs-up
 
2


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image