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JEE Main202313 Apr 2023Morning ShiftMathematicsEllipseActual

Let the tangent and normal at the point 3 3 , 1 on the ellipse x 2 36 + y 2 4 = 1 meet the y - axis at the points A and B respectively. Let the circle C be drawn taking A B as a diameter and the line x = 2 5 intersect C at the points P and Q . If the tangents at the points P and Q on the circle intersect at the point α , β , then α 2 - β 2 is equal to

Options

  1. A61
  2. B60
  3. C304 5
  4. D314 5

Correct answer

C. 304 5

Step-by-step solution

Given that x 2 36 + y 2 4 = 1 Observe that 3 3 , 1 lies on the given ellipse. Equation of tangent to the ellipse at the given point is T : 3 3 x 36 + y 4 = 1 ⇒ 3 x 12 + y 4 = 1 Equation of normal passing through same point will be N : x - 3 3 3 3 36 = y - 1 1 4 ⇒ 12 x - 36 3 3 = 4 y - 4 ⇒ 3 x - 9 3 = 3 y - 3 ⇒ 3 x - 3 y = 8 3 Now tangent and normal intersects the y - axis at A and B respectively. A 0 , 4           B 0 , - 8 Equation of circle with A B as diameter wil

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