0
votes
1answer
37 views

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!
1
vote
1answer
54 views

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. ...
0
votes
1answer
29 views

How to find the equation of a parabola with vertex on the line y = -3x?

Its axis are parallel to the y-axis and passing through (-7,13) and (5,1).
0
votes
2answers
51 views

Find the tangents to the following curve from the given point.

2x^2 + y^2 = 54 from (10,1) P.S. I still don't study calculus. This lesson is from analytic geometry and I have no idea how to solve it because my professor didn't teach it. So if someone could tell ...
0
votes
1answer
33 views

Analytic geometry and calculus question

The tangent to the curve $ x^{0.5} + y^{0.5} = a^{0.5}$ ,$(a>0)$ intersects the $x$ axis in point $M_1$ , and the $y$ axis in point $M_2$. Prove that for any point on the curve $|OM_1|+|OM_2| = ...
1
vote
2answers
24 views

Analytic geometry and calculus combined question

Show that the equation for the tangent with the slope $m$, $(m≠0)$ to the parabola $y^2 = 4px$ is $y = mx + \frac{p}{m}$. How this is done? What is the method for proves of this kind?
2
votes
3answers
38 views

Analytic geometry and calculus mixed question

Find the normal equation to the graph $ y = 2x^2$, that goes through the point $ (1,0.25)$. How this is done? Im not even really sure what I'm being asked here...
0
votes
3answers
46 views

Calculus and analytic geometry question

Find the tangent of the angle in which the functions $x^3 $, and $x^2 $ intersect $(x≠0)$ . I find this question to be quite funny since the intersection point has two tangents going to it, with ...
1
vote
2answers
36 views

Finding the point that a normal line goes through

I have been stumped on a homework problem for quite some time and I'm hoping to get some help with it. The line from the origin to the point $(a, f(a))$ on the graph of $f(x) = \frac1{x^2}$ is ...
-1
votes
1answer
55 views

A problem on circles

Find the equation of the circles passing through two points on the $y$ axis at distances 3 units from the origin and having radius 5. (This a homework problem but I do not know how to solve it.)
0
votes
1answer
70 views

Find the equation of the hyperbola?

The hyperbola being an orthogonal parabola, for which $(-1,2)$ is a focal point and $x-y+1=0$ is an asymptote. If I have the equation for the asymptote $y=x+1$ is the center $(0,1)$? I do not know ...
0
votes
3answers
78 views

2 dimensional coordinate geometry

If $L_1$ and $L_2$ are two lines belonging to the family of lines $(3+2s)x+(4+3s)y=7+5s$ such that they are at maximum and minimum distances from the center of the circle $3x^2 +3y^2 -12x-18y-91=0$, ...
3
votes
2answers
47 views

Proving the following is a Group

I'm studying this weird course called "Analytic Geometry", but in reality it seems like a mash of modern or abstract Algebra (...I'm not so sure...), and includes stuff like Affine transformations, ...
1
vote
1answer
39 views

Ellipse, hyperbola and principle axis

Would anyone mind telling me how to solve (a)? I have no idea what I should do to solve this problem. Also, what is principal axes?
-1
votes
2answers
57 views

Write the equation of a plane that passes point and is parallel to two vectors

Write the equation of a plane that passes point $A(1; -1; 0)$ and is parallel to two vectors $a = (1;1;1)$ and $b = (1; 0; 1)$.
-1
votes
2answers
33 views

Finding the equation of a line without a given slope

Determine the equation of the line that contains the intersection of the lines $-4x+3y=-8$ and $-10x-4y=3$, and that has the same $y$ intercept as the line $$x=-\frac{2}{3y}-\frac{5}{4}$$
0
votes
0answers
53 views

Coordinate Geometry of the Circle

I have a question that I am completely stumped with, I just cannot figure what I need to do. The question is: Circle p has a center (q,w) and a radius r. Circle s touches circle a and b ...
0
votes
0answers
31 views

Proving results about successive reflections of a point in vector geometry

If $Z$ is an arbitrary point in the plane and $$H_A:Z \mapsto 2A-Z$$ ie: $H_A$ denotes the reflection of a point $Z$ at $A$ Prove that for some point $Z$, $$H_A\circ H_B(Z) = 2 \vec{AB}$$ And ...
2
votes
1answer
60 views

Are my answers correct? (finding intercepts, asymptotes, and extrema)

Are my answers correct? a) (0, 4/3) and (2,0) and (-2, 0) b) Horizontal asymptote: $y = 3$, Vertical asymptotes: $x = 3, x = -3$ c) Extremum is at $(0, 4/3)$, maximum.
0
votes
3answers
118 views

Finding coordinates of 4th point in a quadilateral

A(1,5), B(4,0), C(-3,-5) are three vertices of a parallelogram ABCD. Find the coordinates of D, the fourth vertex of the parallelogram *What I've Done:*I've created the structure on a number plane. ...
0
votes
1answer
25 views

Altitudes of a hyperbola

I was doing my engineering graphics assignment and I came across this question A cone of base 60mm diameter and slant height 75mm rests with its base on the horizontal plane. It is cut by an ...
0
votes
1answer
30 views

Prove that the perpendiculars from P,Q,R to BC,CA,AB respectively are also concurrent.

Let $ABC$ and $PQR$ be any two triangles in the same plane,assume that the perpendiculars from the points $A,B,C$ to the sides $QR,RP,PQ$ respectively are concurrent using vector methods or ...
0
votes
2answers
39 views

How to sketch $f(x)= |2x-1|-|1+3x|$

How would you sketch $f(x)= |2x-1|-|1+3x|$? And how would you work out how to sketch it? Please help!
-4
votes
2answers
1k views

Two points: Distance, midpoint, equations of line passing through them and perpendicular line [closed]

Consider two points (-2,3) and (-1,6). Calculate the distance between these two points. Find the midpoint. Obtain the equation of the line passing through the given points. Find the equation of the ...
-3
votes
2answers
50 views

$u= \frac {1}{2i} -\frac 3j$ , find a vector perpendicular to u [closed]

Find the interior angle of the triangle ABC give the point $A(3,4), B(-1,-7), C(-8,-2)$. I am a beginner.
0
votes
1answer
73 views

Problem regarding lines (Analytic Geometry)

Here is the problem: The base of a triangle has a fixed position and its length is constant and measures a. The difference of the squares of the other two sides is constant and measures $b^2$. ...
3
votes
1answer
79 views

Is the result of the actions $\left((\vec A+\vec B) \times (\vec A\times \vec B)\right)\cdot(\vec A \times \vec B)$ depends by $\vec A$ and $\vec B$

I want to show that this action not depend by A and B vectors, I know that cross product of the same vector by itself is $0$. $$\left((\vec A+\vec B) \times (\vec A\times \vec B)\right)\cdot(\vec A ...
0
votes
1answer
1k views

Find plane which parallel to two vectors $L_{1} ( 3,1,10)$ and $L_{2}(1,-1,1)$ passes through a point $M(7,-10,3)$

I`m trying to find a plane which parallel to two vectors $L_{1} ( 3,1,10)$ and $L_{2}(1,-1,1)$ passes through a point $M(7,-10,3)$ what I tried to do is to create $L_{1}L_{2}$ vector then to create ...
2
votes
2answers
635 views

Find the projection of the point on the plane

I want to find the projection of the point $M(10,-12,12)$ on the plane $2x-3y+4z-17=0$. The normal of the plane is $N(2,-3,4)$. Do I need to use Gram–Schmidt process? If yes, is this the right ...
2
votes
2answers
209 views

Find the point of intersection of the straight line $\frac{X+1}{4}=\frac{Y-2}{-2}=\frac{Z+6}{7}$ and plane $3X+8Y-9Z=0$

Find the point of intersection of the straight line $$\frac{X+1}{4}=\frac{Y-2}{-2}=\frac{Z+6}{7}$$ and plane $3X+8Y-9Z=0$ the point of the line is $M(-1,2,-6)$ and direction vector of the line is ...
0
votes
1answer
108 views

Explain what are the projections of the point $P(a,b,c)$ on the planes of the coordinate system.

I want to explain what are the projections of the point $P(a,b,c)$ on the planes of the coordinate system. the meaning is that if it on $XY$ plane so it will be $P(a,b,0)$ and so on? Thanks!
2
votes
2answers
290 views

Check whether the three vectors $A(2,-1,2),B(1,2,-3),C(3,-4,7) $ are in the same plane

I want to check if three vectors are in the same plane, the vectors being $$A(2,-1,2),B(1,2,-3),C(3,-4,7). $$ What I did so far is to create vector $AB ( -1,3,-5)$ and build the plane equation ...
0
votes
0answers
76 views

Explain how to calculate the volume of the parallelepiped $ABCDA_1B_1C_1D_1$ with a mixed product of three vectors.

I`m trying to explain how to calculate the volume of the parallelpiped $ABCDA_1B_1C_1D_1$ with a mixed product of three vectors. I tried to draw it on my note, I need to take 3 vectors but what to ...
0
votes
2answers
63 views

Calculate $\bigtriangleup$ ABC where $A(-2,-3,0)$,$B(-1,0,5)$,$C(4,2,2)$

I want to calculate $\bigtriangleup$ ABC where $A(-2,-3,0)$,$B(-1,0,5)$,$C(4,2,2)$ What I did was to mark the triangle vertices randomly 1) calculate the middle of AB ( I call it G ) to find the ...
2
votes
1answer
33 views

Find the vector by the following criteria

I want to find the vector that meets the following: $$X\parallel (2,1,-1)$$ $$X*(2,1,-1)=3$$ what I did so far is : $$2x+y+z=3$$ I know that parallel vectors the angle is $180$ or $0$. how to ...
0
votes
2answers
67 views

Find the vector that meets the following criteria

I want to find the vector $X$ by the following lines: $$(1,-3,5) \cdot X=49$$ $$(4,1,-1) \cdot X = 0$$ $$(2,0,-3)\cdot X=-9$$ I would like to get some advice how to find him. Thanks!
0
votes
1answer
37 views

For which values ​​of M vectors$A(m-4,2,2m-12),B(2,m-12,2)$ are orthogonal

I want to find for which values ​​of M vectors$A(m-4,2,2m-12),B(2,m-12,2)$ are orthogonal. what I did is to do $A*B=0$ and the result was $m=7$ then I inserted $7$ and tried to check if they are ...
0
votes
1answer
82 views

Proving AB,AC perpendicular to each other when vectors are median

I want to prove this claim: Triangle ABC with $A(2,4,6),B(6,2,2),C(0,0,0)$ median, AC and BC perpendicular to each other. what I did is to the $AB,BC$ make a dot product and thought it will be ...
1
vote
1answer
843 views

Proving a triangle is a right triangle given vertices, using vector dot product

I want to to show that this triangle is a right triangle. I know that the dot of the vectors need to be $0.$ I tried to dot between them but I don't get zero. Claim: Triangle $\bigtriangleup ...
1
vote
0answers
79 views

Draw the locus of points which satisfy the equation

(1) Draw the locus of points $(x,y)$ which satisfy the following equation. $bx^{3}+y^{3}+x^{2}y+bxy^{2}-4abxy-2ab^{2}x^{2}-2ay^{2}+b\left( a^{2}b^{2}+a^{2}-1\right)x+\left( a^{2}b^{2}+a^{2}-1\right) ...
0
votes
2answers
76 views

Coordinate Geometry Problem

I have a question that I've started at school but had couldn't figure out what to do or where to start. Sorry, I don't have the question written down, just the image. ...
2
votes
1answer
84 views

3D Geometry Question

In $3$-dimensional Geometry, if angle made of line segment $OP$ with $X,Y,Z$-axis are in $1:2:3$, then what is the angle made by line segment with $Y$-axis? My Solution: Let $\alpha,\beta$ and ...
0
votes
1answer
117 views

Geometric question?

First of all, is it Geometric? Image of the drafted: I need help solving this question, and I am completely lost on how can I solve this. Could anyone explain the way of solving this geometric ...
2
votes
1answer
96 views

Proof that differential of differential form $=0$ i.e $d(df) = 0$.

Let $f$ be a differentiable function on an open space $U \subset \mathbb{R}^n$. Proove that $d(df) = 0$. So my proof is: Let $$f = \sum c_{i_1, \cdots i_k}(x_*)dx_{i_1} \wedge \cdots ...
0
votes
1answer
43 views

Prove that the $2$ form defines a symplectic structure

Prove that the $2$ form $$\omega = -2[(1+x_2^2)dx_1 \wedge dx_2 + dx_1 \wedge dx_3 + dx_3 \wedge dx_4]$$ defines a symplectic structure on $\mathbb{R}_x^4$. My definition of as ...
2
votes
3answers
1k views

surface area of a sphere above a cylinder

I need to find the surface area of the sphere $x^2+y^2+z^2=4$ above the cone $z = \sqrt{x^2+y^2}$, but I'm not sure how. I know that the surface area of a surface can be calculated with the equation ...
0
votes
0answers
26 views

I get the value of my $2$ form to be $0$.

Let $\omega = (x_1 + \cdots +x_n) \sum_{i<j} dx_i \wedge dx_j$ be a $2$-form on $\mathbb{R}^n, \omega \in \Omega (\mathbb{R}^n)$. Compute the function $$\omega \left( ...
0
votes
1answer
61 views

Sketching the circle for the equation: $\sqrt{(x -1)^2 + (y-1)^2} = \sqrt{2}$

How should I sketch the circle for the equation mentioned in the title? If I calculate the square root of the number $2$ it continues to infinity. $\sqrt2 = 1.414213562...$
1
vote
1answer
121 views

Distance between the two points $P$ and $Q$

Let $d(x,y)$ denote the distance between two points, $x$ and $y$, on the plane. 1) $P(2,9),\quad Q(-1,13)\Rightarrow d(P,Q) = 5.$ 2) $P(1,-2),\quad Q(2,10)\Rightarrow d(P,Q) = \sqrt{145}.$ 3) ...
0
votes
3answers
58 views

Find Distance Between Two Points

If we are to find the distance between the points $P(0,0)$ and $Q(-2,-3)$, then we can use the Theorem of Pythagoras for this purpose. $distance (P,Q) = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$ ...