Q82 / 155 · WBJEE 2020 · Mathematics

The equation of the latus rectum of a parabola is $x+y=8$ and the equation of the tangent at the vertex is $x+y=12$. Then the length of the latus rectum is

  • A
    $4 \sqrt{2}$ unit
  • B
    $2 \sqrt{2}$ unit
  • C
    8 unit
  • Correct answer
    D
    $8 \sqrt{2}$ unit

Solution

Hint: The distance between latus rectum and equation of tangent at vertex is 'a'. Here $\mathrm{a}=\frac{4}{\sqrt{1+1}}=2 \sqrt{2}$ So, length of latus rectum $=4 \mathrm{a}=8 \sqrt{2}$ unit

Hence, the correct answer is option: 'D'.

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