TS EAMCET · Maths · Parabola
If the line segment joining the vertex of the parabola \(y^2=4 a x\) and a point on the parabola, makes an angle \(\theta\) with the positive \(X\)-axis, then the length of that line segment is
- A \(\frac{4 a \sin \theta}{\cos ^2 \theta}\)
- B \(\frac{4 a \cos \theta}{\sin ^2 \theta}\)
- C \(4 a \sin \theta \cdot \cos ^2 \theta\)
- D \(4 a \cos \theta \cdot \sin ^2 \theta\)
Answer & Solution
Correct Answer
(B) \(\frac{4 a \cos \theta}{\sin ^2 \theta}\)
Step-by-step Solution
Detailed explanation
Equation of given parabola is \(y^2=4 a x\) having vertex \(V(0,0)\) Let a point on the parabola \(P\left(a t^2, 2 a t\right)\), so slope of line joining point \(V(0,0)\) and \(P\left(a t^2, 2 a t\right)\) is \(\frac{2 a t-0}{a t^2-0}=\tan \theta\) (given)…
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