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The lines y=2 x+ 76 and 2 y+x=8 touch the ellipse x^2 16 + y^2 12 =1 . If the point of intersection of these two lines lie on a circle. whose centre coincides with the centre of that ellipse, then the equation of that circle is

Options

  1. Ax^2+y^2=28
  2. Bx^2+y^2=16
  3. Cx^2+y^2=12
  4. Dx^2+y^2=(4+ 8 )^2

Correct answer

A. x^2+y^2=28

Step-by-step solution

Given, equation of tangents to the ellipse are, aligned & y=2 x+ 76 and 2 y+x=8 y=- 1 2 x+4 & m₁=2 and m₂=-- & Here, m₁ m₂=-1 aligned It means that the given tangents are perpendicular to each other. Thus, required circle will be the director circle to ellipse. Hence, required equation of circle is aligned x^2+y^2 & =a^2+b^2=16+12 x^2+y^2 & =28 aligned

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