14
votes
Accepted
Difficulties with Set-Notation in Taxicab Geometry
…the set of points $P$ that is the answer is dependent on the distance between $A$ and $B$, thus I am to observe some property of the relationship between the sum of circles, which hardly makes sense ...
- 1,321
12
votes
Difficulties with Set-Notation in Taxicab Geometry
This is not about "adding sets" (though such a notion does exist—you might search the term "Minkowski sum"). Rather, the set is defined by an equation, and you are being asked to ...
- 34k
11
votes
Difficulties with Set-Notation in Taxicab Geometry
As @XanderHenderson notes in his excellent answer, this is not about adding sets, it's about adding distances - in this case taxicab distances. It's not about circles either.
One way to think of the ...
- 109k
5
votes
Accepted
Maximizing the area of the triangle determined by foci of three parabolas, each touching all the three lines $x=0,y=0,x+y=2$
Observe that the point in $(4)$ is a point on the circle $x^2+y^2 = 2(x+y)$, i.e. $(x-1)^2+(y-1)^2=2$, with center $(1,1)$ and radius $r=\sqrt2$. We check this shortly starting from the relation $\...
- 40.7k
2
votes
Counting intersection points where multiple equations coincide at least twice (is there a known framework?)
Hint for deriving the main equation $x^2 + y^2 = a^2$: Square $x = a \cos \theta$ and $y = a \sin \theta$, then add both together, and remember the Pythagorean Identity $\cos^2 \theta + \sin^2 \theta ...
- 4,395
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