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JEE Advanced2006MathematicsParabolaActual

Paragraph: Read the following passage and answer the questions. Let A B C D be a square of side length 2 units. C₂ is the circle through vertices A, B, C, D and C₁ is the circle touching all the sides of square A B C D . L is the line through A . Question: A line M through A is drawn parallel to B D . Points S moves such that its distances from the line B D are the vertex A are equal. If locus of S cuts M at T₂ and T

Options

  1. A1 2 sq unit
  2. B2 3 sq unit
  3. C1 sq unit
  4. D2 sq unit

Correct answer

C. 1 sq unit

Step-by-step solution

A G= 2 A T₁=T₁ G= 1 2 as A is the focus, T₁ is the vertex and B D is the directrix of parabola. Also, T₂ T₃ is latus rectum aligned & T₂ T₃=4 1 2 & Area of T₁ T₂ T₃= 1 2 1 2 4 2 =1 sq unit aligned

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