-1
votes
1answer
12 views

Equation of a line with a positive gradient [on hold]

Two straight lines passing through the point (0,2) are tangent to the graph of the function y=1-x^2. Find the equation of the line with a positive gradient.
-6
votes
0answers
26 views

Need a solution to find the locus of an equation. [on hold]

Find the equation of the locus of a point which moves so that its distance from $(a,0)$ is equal to its distance from the $y$-axis. The answer is $$y^2 - 2ax + a^2 =0$$ Please can someone find the ...
0
votes
3answers
48 views

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 ...
1
vote
2answers
103 views

Omitting $i$ in calculations

Is it possible in various calculations related to the complex plane which also include analytic geometry , calculating distances etc, to omit $i$ and treat the imaginary axis as simply the cartesian ...
1
vote
1answer
31 views

Doubt on locus of a median point

I'm learning about geometric locus and ain't had an good time, I'm struggling with this problem: By the way, any study resource on geometric locus is welcome! Given an segment $AB$ formed by points ...
0
votes
1answer
32 views

Graphs interpretation question

Suppose we have a prarbola $y^2 = 2px$ ....this is in fact $y = \sqrt{2px}$, so we plot it like a square root function, so it has no applied values for less than zero. However I saw in my textbook ...
1
vote
2answers
73 views

Find an unknown coefficient in a line equation…

So, I have to find the unknown coefficient in this line: $$x+y+C=0$$ so that it is a tangent to this circle: $$x^2+y^2-5x-7y+6=0$$ I've transformed the circle equation to this form: ...
0
votes
1answer
68 views

How do i find the radius and the center of these circles

Please help me with my math Radius Homework Help is really appreciated! PS: Pls Don't be bothered by my erasure on my sheet, those 4 question are unanswered. Instructors' formula is x^2 + y^2 = r^2 ...
0
votes
0answers
43 views

Center of circumscribed circle of a triangle

I've been given the parametric equations of the height, median and inner angle bisector through the point $A$ of a triangle $\triangle{ABC}$: $$ h: \begin{cases}x = 2 - s \\ y = 1 \\ z = -3 + 2s ...
3
votes
1answer
43 views

Area enclosed between half lines in polar space

I don't know if the anwser to my question is obvious because I cannot find any explanation anywhere on google. Question The blue region $R$ is bounded by the curve C with equation $r^{2} = ...
1
vote
0answers
42 views

building a polytop from polytop and finding its volume

Let $P$ be a symmetric polytope with $M$ vertices. Suppose we subdivide this polytope into $M$ equal parts $A_i, i=1, \ldots, M$ such that each part $A_i$ correspond to one vertex, $v_i, i=1, \ldots, ...
0
votes
1answer
16 views

About a/the definition of plane.

Let $P$ be a point in 3-space and consider a located vector $ \overrightarrow {0N}$. We define the plane passing through $P$ perpendicular to $ \overrightarrow {0N}$ to be the collection of all ...
1
vote
1answer
51 views

Conic Sections and Complex numbers

If $\omega$ is a complex number such that |$\omega$| does not equal 1, then the complex number $$z = \omega + \frac{1}{\omega}$$ describes a conic. The distance between the foci of the conic described ...
0
votes
0answers
21 views

analytic gemotry circles question

Let there be 2 circels; Suppose we want them to intersect in a rihgt angle, what should we require of them? any (construcive and well based) hints would be helpful.
0
votes
1answer
33 views

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 ...
2
votes
3answers
164 views

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 $ ?
1
vote
0answers
30 views

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 ...
0
votes
1answer
49 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
65 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
71 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
56 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
30 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
52 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
66 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
63 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 ...
0
votes
1answer
21 views

Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
-1
votes
1answer
57 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
76 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
86 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
48 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
55 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
3answers
52 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
66 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
48 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
63 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
302 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. ...
1
vote
1answer
62 views

find equation of a plane P containing 2 points and parallel to a cross vector

Given: A(0,3,1), B(1,1,4), A'(0,1,0), B'(1,-3,3). Find the equation of plane (P) containing A and B and parallel to the vector AB x A'B'. Find the equation of plane (Q) containing A' and B' and ...
0
votes
1answer
26 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
31 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
40 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
51 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
79 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
82 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
718 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
238 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
154 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
434 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 ...