TS EAMCET · Maths · Straight Lines
Two points \(A(-a, 0)\) and \(B(a, 0)\) are given. If \(C\) is a variable point lying on one side of the line \(A B\) such that \(\angle C A B-\angle C B A=\alpha\), where \(\alpha\) is a positive constant, then locus of the point \(C\) is
- A \(a^2+x^2+y^2+2 x y \cot \alpha=0\)
- B \(a^2-x^2+y^2+2 x y \cot \alpha=0\)
- C \(a^2-x^2-y^2+2 x y \tan \alpha=0\)
- D \(a^2-x^2+y^2+2 x y \tan \alpha=0\)
Answer & Solution
Correct Answer
(B) \(a^2-x^2+y^2+2 x y \cot \alpha=0\)
Step-by-step Solution
Detailed explanation
Given Let \(C(x, y)\) Slope of \(A B=0\) \( \begin{aligned} \therefore \tan \beta & =\text { Slope of } A C \\ \therefore \tan \beta & =\frac{y}{x+a} \end{aligned} \) Slope of \(B C=\tan (\pi-\gamma)\)…
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