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AP EAMCET202316 May 2023Evening ShiftMathematicsEllipseActual

If a focal chord of the ellipse x^2 25 + y^2 16 =1 meets its minor axis at the point (0,3) , then the perpendicular distance from the centre of the ellipse to this focal chord is

Options

  1. A5
  2. B2 5
  3. C1
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Let A=(0,3) Given the ellipse, x^2 25 + y^2 16 =1 So focus of the ellipse F= ( 5^2-4^2 , 0 ) F =(3,0), P ( 0+3 2 , 3+0 2 )= ( 3 2 , 3 2 ) So required distance = ( 3 2 )^2+ ( 3 2 )^2 = 18 4 = 9 2 = 3 2

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