AP EAMCET · Maths · Parabola
If a chord of the parabola \(y^2=4 x\) passes through its focus and makes an angle \(\theta\) with the \(X\)-axis, then its length is
- A \(4 \cos ^2 \theta\)
- B \(4 \sin ^2 \theta\)
- C \(4 \operatorname{cosec}^2 \theta\)
- D \(4 \sec ^2 \theta\)
Answer & Solution
Correct Answer
(C) \(4 \operatorname{cosec}^2 \theta\)
Step-by-step Solution
Detailed explanation
Let \(P\left(t^2, 2 t\right)\) be the one end of a focal chord \(P Q\) of the parabola \(y^2=4 x\), the coordinate of the other end \(Q\) are \(\left(\frac{1}{t^2}, \frac{-2}{t}\right)\). \(\left[\because t t^{\prime}=-1\right]\) Given, the chord makes a \(\theta\) with positive…
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