yaworsw/euler-manager

---
:id: 246
:name: Tangents to an ellipse
:url: https://projecteuler.net/problem=246
:content: "A definition for an ellipse is:  \nGiven a circle c with centre M and radius
  r and a point G such that d(G,M)\\<r, the locus of the points that are equidistant
  from c and G form an ellipse.\n\nThe construction of the points of the ellipse is
  shown below.\n ![]({{ images_dir }}/p246_anim.gif)\n\nGiven are the points M(-2000,1500)
  and G(8000,1500).  \n Given is also the circle c with centre M and radius 15000.
  \ \nThe locus of the points that are equidistant from G and c form an ellipse e.
  \ \nFrom a point P outside e the two tangents t<sub>1</sub> and t<sub>2</sub> to
  the ellipse are drawn.  \nLet the points where t<sub>1</sub> and t<sub>2</sub> touch
  the ellipse be R and S.\n\n ![]({{ images_dir }}/p246_ellipse.gif)\n\nFor how many
  lattice points P is angle RPS greater than 45 degrees?\n\n"