WBJEE · Maths · Straight Lines
The line joining \(A(b \cos \alpha, b \sin \alpha)\)
and
\(B(a \cos \beta, a \sin \beta),\) where \(a \neq b,\) is produced to the
point \(M(x, y)\) so that \(A M: M B=b: a\). Then, \(x \cos \frac{\alpha+\beta}{2}+y \sin \frac{\alpha+\beta}{2}\) is equal to
- A 0
- B 1
- C -1
- D \(a^{2}+b^{2}\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Since, \(A M: B M=b: a\) \(\therefore M\) divides \(A B\) extemally in the ratio \(b: a\)...(i) \(\therefore \quad x=\frac{b \cdot a \cos \beta-a b \cos \alpha}{b-a}\) \(y=\frac{b a \sin \beta-a b \sin \alpha}{b-a}\) (ii) Divide Eq. (i) by Eq, (ii), we get…
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