WBJEE · Maths · Hyperbola
Let \(A(-1,0)\) and \(B(2,0)\) be two points. \(A\) point \(M\) moves in the plane in such a way that \(\angle M B A=2 \angle M A B .\) Then, the point \(M\) moves along
- A a straight line
- B a parabola
- C an ellipse
- D a hyperbola
Answer & Solution
Correct Answer
(D) a hyperbola
Step-by-step Solution
Detailed explanation
\begin{array}{l} \text { Let } \angle M A B=\theta \text { , then } \angle M B A=2 \theta \\ \text { tan } \theta=\frac{k}{1+h} \text { and } \tan 2 \theta=\frac{k}{2-h} \\ \text { then } \tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^{2} \theta}=\frac{k}{2-h} \\ \Rightarrow \quad…
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