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JEE Main 202228 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2022 · 28 June · Evening Shift · Mathematics · Parabola

If vertex of parabola is (2, - 1) and equation of its directrix is...

If vertex of parabola is (2,−1)\left(2, - 1\right) and equation of its directrix is 4x−3y=214x - 3y = 21, then the length of latus rectum isIf vertex of parabola is (2, - 1) and equation of its directrix is 4x - 3y = 21 , then the length of latus rectum is

Options

  1. A22
  2. B88
  3. C1212
  4. D1616

Correct answer

B. 88

Step-by-step solution

Plotting the graph with given data we have,

If vertex of parabola is (2, - 1) and equation of its directrix is 4x - 3y = 21 , then the length of latus rectum is

We know that, in any parabola, the length of the latus rectum =4a= 4a and perpendicular distance from vertex to the directrix =a= a

So, a=∣8+3−2142+(−3)2∣a = \left|\dfrac{8 + 3 - 21}{\sqrt{{4}^{2} + {\left(- 3\right)}^{2}}}\right|

⇒a=∣−105∣=2⇒ a = \left|\dfrac{- 10}{5}\right| = 2

Therefore, the length of the latus rectum 4a=4×2=84a = 4 \times 2 = 8

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