Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2017 · 9 April · Online · Mathematics · Parabola

If y = mx + c is the normal at a point on the parabola y ^ 2 = 8x...

If y=mx+cisthenormalatapointontheparabolay = mx + c is the normal at a point on the parabola{y}^{2} = 8xwhosefocaldistanceiswhose focal distance is8units,then∣c∣units, then \left|c\right| is equal to:

Options

  1. A838\sqrt{3}
  2. B10310\sqrt{3}
  3. C232\sqrt{3}
  4. D16316\sqrt{3}

Correct answer

B. 10310\sqrt{3}

Step-by-step solution

Let the point on the parabola be P(at2,2at)P( a{t}^{2} , 2at ) where a=2.a = 2.

Given distance of this point from focus be 88 units

⇒(at2−a)2+4a2t2=64⇒ {\left(a{t}^{2} - a\right)}^{2} + 4{a}^{2}{t}^{2} = 64

⇒(a(t2+1))=8⇒ \left(a\left({t}^{2} + 1\right)\right) = 8

⇒t2+1=4⇒t2=3⇒ {t}^{2} + 1 = 4 ⇒ {t}^{2} = 3

⇒t=±3⇒ t = \pm \sqrt{3}

Since y=mx+cy = mx + c is normal to the parabola

⇒c=2at+at3⇒ c = 2at + a{t}^{3}

⇒∣c∣=103⇒ \left|c\right| = 10\sqrt{3}
Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the… JEE Advanced 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs