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PROBABILITY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPROBABILITY1 Mark
MCQ
The equation of directrix and latus rectum of a parabola are 3x - 4y + 27 = 0 and 3x - 4y + 2 = 0. Then the length of latus rectum is:
  • A
    5
  • ✓
    10
  • C
    15
  • D
    20
✓

Answer

Correct option: B.
10
  1. 10
Solution:
$\text{d}=\frac{\text{c}_1-\text{c}_2}{\sqrt{\text{a}^2+\text{b}^2}}$
where dd is the distance between lines whose equations are $a x+b y+C_1=0 \& a x+b y+C_2=0$
$\text{d}=\frac{27-2}{\sqrt{4^2+3^2}}$
= 5 d = 5
If the distance between vertex and latus rectum = distance of vertex from directri x = a
= then d = 2a = 5
⇒ Length of latus rectum = 4a = 10

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