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Parabola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSParabola1 Mark
MCQ
The length of the latus-rectum of the parabola $x^2 - 4x - 8y + 12 = 0$ is
  • A
    4
  • B
    6
  • ✓
    8
  • D
    10
✓

Answer

Correct option: C.
8
  1. 8
Solution:
Given:
$x^2 - 4x - 8y + 12 = 0$
$(x - 2)^2 - 8y + 8 = 0$
$(x - 2)^2 = 8y - 8 = 8(y - 1)$
Let $X = x - 2, Y = y - 1$
$\therefore X^2 = 8Y$
$\therefore$ Length of the latus rectum = $4a = 8$ units

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