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The length of the latus rectum of the curve represented by x = 3 cos ⁡ t + sin ⁡ t and y = 4 cos ⁡ t - sin ⁡ t , is

Options

  1. A9 2 units
  2. B9 2 units
  3. C32 2 3 units
  4. D9 2 units

Correct answer

D. 9 2 units

Step-by-step solution

x 3 = cos ⁡ t + sin ⁡ t and y 4 = cos ⁡ t - sin ⁡ t x 3 2 + y 4 2 = 2 x 2 3 2 2 + y 4 2 2 = 1 Hence, the length of the latus rectum = 2 3 2 2 4 2 = 9 2

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