1.7 KiB
1.7 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4621000cf542c50ff75 | Problem 246: Tangents to an ellipse | 5 | 301893 | problem-246-tangents-to-an-ellipse |
--description--
A definition for an ellipse is:
Given 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.
The construction of the points of the ellipse is shown below.
Given are the points M(-2000, 1500)
and G(8000, 1500)
.
Given is also the circle c
with centre M
and radius 15\\,000
.
The locus of the points that are equidistant from G
and c
form an ellipse e
.
From a point P
outside e
the two tangents t_1
and t_2
to the ellipse are drawn.
Let the points where t_1
and t_2
touch the ellipse be R
and S
.
For how many lattice points P
is angle RPS
greater than 45°?
--hints--
tangentsToAnEllipse()
should return 810834388
.
assert.strictEqual(tangentsToAnEllipse(), 810834388);
--seed--
--seed-contents--
function tangentsToAnEllipse() {
return true;
}
tangentsToAnEllipse();
--solutions--
// solution required