# Tagged Questions

Questions on the use of algebraic techniques to prove geometric theorems.

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### Permutation Combination

Let $C = \{(i, j)|i, j \in \mathbb Z,\; 0 ≤ i, j ≤ 24\}$. How many squares can be formed in the plane all of whose vertices are in $C$ and whose sides are parallel to the X−axis and Y − axis?
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### Angle bisectors for pair of lines

Suppose you have a pair of lines passing through origin, ax^2 + 2hxy +by^2 = 0, how would you find the equation of pair of angle bisectors for this pair of lines. I can do this for 2 separate lines, ...
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### Equilateral triangle inscribed in a ellipse

"Given any point on a ellipse, is it always possible to inscribe an equilateral triangle, with a vertex coincident with that point, in the ellipse?" I thought I could use analytical geometry, but ...
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### Geometric interpretation of a complex solution

A straight line in 2-D $x+y=3$ and a circle in 2-D $x^2+y^2=4$ do not have a point of intersection in the plane containing the two. But on solving these equations analytically, on gets 2 complex ...
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### Equation of horizontal/vertical line and changing to $y=mx+c$ format

I've been given the equation $2x-3y=5$. I was wondering whether this is a horizontal or vertical equation and how would I rearrange this to $y=mx+c$. I know that this is a fairly basic equation but ...
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### Tensor notation (practicing)

I'm praticing tensor notation, and I want to prove this way that given vectors $A,B,C,D$ then $(A \times B) \times (C \times D) = \det(A,C,D)B - \det(B,C,D)A$, where $\det$ means the triple product. I'...
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### List of topics for basic calculus (1st,2nd,3rd semester)

I am an computer science student, currently studying in 2nd semester. Therefore my math courses are pretty weak. Although I "aced" them, I still feel I could use some extra basic calculus knowledge in ...
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### Analytic Geometry

How does one solve: Find the equation of the circle which has it's center on the line $y= 3-x$ , and which has as tangents the lines $2y-x = 22,$ $2x+y=11$ ?
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### Circle Tangent question

I would like to ask for assiatance on the following: Find the eqation of a circle, with a radius of$\sqrt 2$ , which also has as tangetns the lines: $y=x+2$ , $y=-7x$. It is known that the ...
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### Maximize the distance between a point and a bounding rectangle

There are $n$ random points in the $x-y$ plane, whose coordinates are known beforehand. We can use a minimum bounding rectangle (MBR) to bound these points. In this scenario, the MBR can be rotated, ...
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### Check my solution to this trig inequality

Problem $1.88$ : Solve $$\cos x\lt \frac{\sqrt{3}}{2},\qquad x \in [0,2\pi]$$ I found the set of solutions to be $S=[0,2\pi]-\left[\dfrac{\pi}{6},\dfrac{11\pi}{6}\right]$ Is this correct? Thank you.