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JEE Main 201212 MayOnline
Exam
JEE Main
Year
2012
Date
12 May
Mode
Online
Subject
Mathematics
Chapter
Parabola

JEE Main 2012 · 12 May · Online · Mathematics · Parabola

The area of triangle formed by the lines joining the vertex of the...

The area of triangle formed by the lines joining the vertex of the parabola, x2=8yx^2=8 y, to the extremities of its latus rectum isThe area of triangle formed by the lines joining the vertex of the parabola, x^2=8 y , to the extremities of its latusThe area of triangle formed by the lines joining the vertex of the parabola, x^2=8 y , to the extremities of its latus

Options

  1. A2
  2. B8
  3. C1
  4. D4

Correct answer

B. 8

Step-by-step solution

Given parabola is x2=8y⇒4a=8⇒a=2\mathrm{x}^2=8 \mathrm{y}\Rightarrow 4 a=8 \Rightarrow a=2 To find: Area of △ABC\triangle A B CA=(−2a,a)=(−4,2)B=(2a,a)=(4,2)C=(0,0)\begin{aligned}& A=(-2 a, a)=(-4,2) \\ & B=(2 a, a)=(4,2) \\ & \mathrm{C}=(0,0) \end{aligned}The area of triangle formed by the lines joining the vertex of the parabola, x^2=8 y , to the extremities of its latus\\∴ Area =12∣−421421001∣=12[−4(2)−2(4)+1(0)]=−162=−8≈8 sq. unit (∵ area cannot be negative )\begin{aligned}& \therefore \text{ Area }=\frac{1}{2}\left|\begin{array}{ccc} -4 & 2 & 1 \\ 4 & 2 & 1 \\ 0 & 0 & 1 \end{array}\right| \\ & =\frac{1}{2}[-4(2)-2(4)+1(0)] \\ & =\frac{-16}{2}=-8 \approx8 \text{ sq. unit }\\ & (\because \text{ area cannot be negative })\end{aligned}$
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