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Paragraph: Tangents are drawn from the point P(3,4) to the ellipse x^2 9 + y^2 4 =1 touching the ellipse at points A and B . Question: The equation of the locus of the point whose distance from the point P and the line A B are equal, is

Options

  1. A9 x^2+y^2-6 x y-54 x-62 y +241=0
  2. Bx^2+9 y^2+6 x y-54 x+62 y -241=0
  3. C9 x^2+9 y^2-6 x y-54 x-62 y -241=0
  4. Dx^2+y^2-2 x y+27 x+31 y -120=0

Correct answer

A. 9 x^2+y^2-6 x y-54 x-62 y +241=0

Step-by-step solution

Equation of A B is y-0=- 1 3 (x-3) gathered x+3 y-3=0 |x+3 y-3|^2=10 [(x-3)^2+(y-4)^2 ] gathered (Look at coefficient of x^2 and y^2 in the answers)

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