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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

Let the focus S of the parabola y^ 2 =8 x lies on the focal chord...

Let the focus SS of the parabola y2=8xy^{2} =8 x lies on the focal chord PQPQ of the same parabola. If PS=6,PS = 6, then the square of the slope of the chord PQPQ& is

Options

  1. A25\dfrac{2}{\sqrt{5}}
  2. B45\dfrac{4}{5}
  3. C54\dfrac{5}{4}
  4. D94\dfrac{9}{4}

Correct answer

B. 45\dfrac{4}{5}

Step-by-step solution

We know that, PS,4,SQPS, 4, SQ are in H.P.H. P.
⇒16,14,1SQ⇒ \dfrac{1}{6}, \dfrac{1}{4}, \dfrac{1}{SQ} are in A.P.A. P.
⇒1SQ=24−16=13⇒SQ=3⇒ \dfrac{1}{SQ} = \dfrac{2}{4} - \dfrac{1}{6} = \dfrac{1}{3} ⇒ SQ = 3
⇒PQ=6+3=9=4cosec2θ⇒ PQ = 6 + 3 = 9 = 4cosec^{2}\theta (where, tanθtan \theta is the slope of PQPQ )
⇒1+cot⁡2θ=94⇒cot⁡2θ=54⇒ 1 + \cot^{2} \theta = \dfrac{9}{4} ⇒ \cot^{2} \theta = \dfrac{5}{4}
⇒tan⁡2θ=45⇒ \tan^{2} \theta = \dfrac{4}{5}
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