WBJEE · Maths · Parabola
The length of the chord of the parabola \(y^{2}=4 a x(a>0)\) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola is
- A \(\pm 4 a \cot \alpha \operatorname{cosec} \alpha\)
- B \(4 a \cot \alpha \operatorname{cosec} \alpha\)
- C \(-4 a \cot \alpha \operatorname{cosec} \alpha\)
- D \(4 a \operatorname{cosec}^{2} \alpha\)
Answer & Solution
Correct Answer
(B) \(4 a \cot \alpha \operatorname{cosec} \alpha\)
Step-by-step Solution
Detailed explanation
Hint: Equation of OP:- \(y=x \tan \alpha\) Solving with \(y^{2}=4 a x\), we get : \(x^{2} \tan ^{2} \alpha=4 a x \quad \Rightarrow x=4 a \cot ^{2} \alpha\) Substituting, \(y=4 a \cot \alpha\)…
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