# Tagged Questions

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### Rotation around a line which is determined by two points in 3D space

If we have three points like $A(x_1,y_1,z_1)$, $B(x_2,y_2,z_2)$ and $C(a,b,c)$. Then, $A$ and $B$ determines a line like $l$. After that, we rotate $C$ around $l$ by $\omega$ degree (anti-clockwise). ...
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### A book on analytic geometry

It's easy to find good recommendation for books here for any subject other than analytic geometry ,therefore I'd like to ask for any suggestion of analytic geometry books ,the only charactrestic I'm ...
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### Lines joining origin to points of intersection of two conics

If the lines joining origin and point of intersection of curves $$ax^2+2hxy+by^2+2gx=0$$ and $$a_1x^2+2h_1xy+b_1y^2+2g_1x=0$$ are mutually perpendicular, then prove that $$g(a_1+b_1)=g_1(a+b)$$ How ...
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### Help with simple rotation on an x,y plane

I'm a programmer, with too little background in mathematics, and I am currently faced with the challenge of rotating an object on a 2 axis plane. Something that is hopefully quite easy for you guys. ...
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### Doubts on locus and its equation

"Find the equation to the locus of a point which is collinear with points $M(a,0)$ and $N(0,b)$." The answer is $- x/a + y/b$. How I tried to find the solution: $P$ is a point whose assigned ...
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### Equation for the length of a chord parallel to either the minor or major axis in an ellipse

I am looking for a way to compute the length of any chord parallel to the minor (or major) axis of an ellipse. In all cases I know the lengths of both axes, and the distance between the chord and axis ...
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### getting the slopes of the sides of an equilateral triangle given 2 points

I want to get the slopes of an equilateral triangle given the 2 vertices. Let's say they are (0, 0) and (5, 5). Graphing this would give 2 triangles forming a diamond. I tried to use distance formula ...
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### Closest Point on a Sphere to Another Point

Given a sphere $S(c,r)$, $c$ being the center point $(x,y,z)$ and $r$ being the radius, there is a point $p(x', y', z')$ which is either inside or outside $S$. I want to find the point $q$ such that ...
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### $\frac{|| \overline{AM}||}{|| \overline{AB}||}=\frac{|| \overline{AN}||}{|| \overline{AC}||}=\frac{|| \overline{MN}||}{|| \overline{BC}||}$

$\Delta ABC$ is a triangle, $M$ is a point in the segment $\overrightarrow{AB}$ and $N$ is a point in the segment $\overrightarrow{AC}$, such that $\overrightarrow{MN}$ is parallel to ...
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### Finding an equation of circle which passes through three points

How to find the equation of a circle which passes through these points $(5,10), (-5,0),(9,-6)$ using the formula $(x-q)^2 + (y-p)^2 = r^2$. I know i need to use that formula but have no idea how to ...
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### Finding the equation of a plane in 3-D by using point-to-point distances

Assume that we have a plane $P(a,b,c,d)$ whose equation is unknown. We know that there is a point set $N = \{n_1, n_2, ...\}$ and $\forall n_i \in N$, $n_i$ is on $P$. Also, $\forall n_i, n_j \in N$, ...
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### The relation between the radiuses…

Find $\frac{R}{r}$ where $R$ is the radius of the circumscribed circle of a trapezoid and $r$ is the radius of the inscribed circle of this trapezoid. Thank you!
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### Problem concerning inscribed and circumscribed circles…

Can you please help me solve this really difficult problem: Find R/r where R is the radius of the circumscribed circle of a trapezoid and r is the radius of the inscribed circle of this trapezoid. ...
consider 2 triangles like $\bigtriangleup ABC \quad and \quad \bigtriangleup \acute{A}\acute{B}\acute{C}$, which $S_{\bigtriangleup \acute{A}\acute{B}\acute{C}} \leq S_{\bigtriangleup ABC}$.(S stands ...