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MHT CET202613 April 2026Morning ShiftMathematicsParabolaActual

The area of the triangle formed by the lines joining the vertex of the parabola x^2 = 48y to the ends of its latus rectum, is .....

Options

  1. A144 sq. units
  2. B288 sq. units
  3. C72 sq. units
  4. D576 sq. units

Correct answer

B. 288 sq. units

Step-by-step solution

The given equation of the parabola is x^2 = 48y . Comparing this with the standard form x^2 = 4ay , we get 4a = 48 , which gives a = 12 . The vertex of the parabola is O(0, 0) . The ends of the latus rectum for x^2 = 4ay are (2a, a) and (-2a, a) . Substituting a = 12 , the ends of the latus rectum are L(24, 12) and L'(-24, 12) . The area of the triangle formed by the vertex and the ends of the latus rectum is given by 1 2 base height . The base is the length of the latus rectum LL' = 4a = 48 . The height is the dis

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