0
votes
2answers
39 views

What is the y-cooridinate for the point on the curve with x-cooridante 20?

What is the y-coordinate for the point on the curve with x-coordinate 20? $F. 160$ $G. 162$ $H. 164$ $J. 166$ $K. 168$ The explanation says "The correct answer is G. If the x-coordinate is 20, ...
1
vote
2answers
28 views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
8
votes
3answers
131 views

Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane.

I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines ...
0
votes
1answer
71 views

Check if point lies on a line segment

I know there are shorter solutions that use dot product, but I don't know what the logic behind doing so involves so I came up with something that I understand myself (i will research the dot product ...
-1
votes
1answer
50 views

How to find coordinates of a point on a 3D cylinder in Cartesian system if any one point on cylinder and dimensions of cylinder are known?

Consider a cylinder of known dimensions inserted in 3D cartesian space. I know the cartesian coordinate of one point located on the surface of cylinder. Using this information I want to find out the ...
1
vote
1answer
472 views

Express spherical coordinates with different centers in terms of each other.

Imagine that you have two spheres with a distance $R$ from one center to the other one. Now, it is well known how one would get the cartesian position vector of each point in sphere 1 by using ...
-1
votes
1answer
61 views

The smallest value of $|a|$ such that the lines $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent

Question If the line $ x = a+m $, $y = -2 $ and $y = mx$ are concurrent, the least value of $|a|$ is (A) $\sqrt{2}$ (B) $2\sqrt{2}$ (C) $2\sqrt{3}$ (D) $3\sqrt{2}$ Solution Since the ...
1
vote
1answer
178 views

Linear Transformation of a straight line

Let $L_{1}: x-y-2=0$ be a straight line in the x-y coordinate system. Find a coordinate system $(x_{1},y_{1})$ having its origin at $(0,0)$ and relative to which $L_{1}$ has equation $y_{1}= ...
0
votes
1answer
94 views

plot a point which is in form of lat and long in a pixel map

I need to plot a point which is in form of lat and long this point is equivalent to a screen coordinate on pixels on my map. I want to make a relation in these two point so if you want to plot a ...
1
vote
0answers
129 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
0
votes
2answers
538 views

Linear equations; how to write an equation from given coordinates?

A straight line goes through the points $( 0, 1 )$, $( 2, 7 )$ and $( 4, 13 )$ and I need to write the equation of this straight line. How do you write equations? I know you have it's usually $y = x ...
2
votes
3answers
74 views

Find at least two ways to find $a, b$ and $c$ in the parabola equation

I've been fighting with this problem for some hours now, and i decided to ask the clever people on this website. The parabola with the equation $y=ax^2+bx+c$ goes through the points $P, Q$ and $R$. ...
2
votes
2answers
111 views

question on transformation

If a $2$d coordinate transformation function is given by $f(x,y)= 3x+1$, then what does it mean? How do I calculate the transformed coordinates for the points say $(3,4)$ in the initial space?
2
votes
1answer
126 views

A Question About Linear Interpolation

So lets say I have two points $A=(x_1, y_1, z_1)$ and $B=(x_2, y_2, z_2)$. $A$ and $B$ are each associated with some scalar value $K_1$ and $K_2$. $K_1$ is negative and $K_2$ is positive and all the ...
2
votes
3answers
1k views

The area of the triangle with vertices (3, 2), (3, 8), and (x, y) is 24. What is x?

The area of the triangle with vertices (3, 2), (3, 8), and (x, y) is 24. A possible value for x is: a) 7 b) 9 c) 11 d) 13 e) 15 Please show your work and explain.
2
votes
3answers
122 views

Finding the number of points on the straight line joining $(-4,11)$ and $(16,-1)$

Find the number of points on the straight line which joins $(-4,11)$ and $(16,-1)$ whose coordinates are positive integers. a) $1$ b) $2$ c) $3$ d) $4$
1
vote
3answers
147 views

How do I calculate a change of coordinates given two lines as new axis?

Suppose we have an old coordinate system using the variables $x$ and $y$. We are given two equations for lines to form the axis for new coordinates. e.g. The line $z=0$ is given by the equation $y = ...
0
votes
1answer
113 views

Find the number of common normals to both these curves.

Find the number of common normals to the curves $ x^2 + (y-1)^2 =1 $ and $y^2=4x$. My take : I formed a cubic in $m$ i.e. slope, so there'll be 3 normals. Please help.
0
votes
2answers
80 views

how to truncate a line along the same slope at a given boundary?

Let's say I have a 2D coordinate space defined by $-5 \leq x,y \leq 5$. Then let's say I have coordinates $(x_1,y_1)$ and $(x_2,y_2)$ for a line that will run from $(4,4)$ to $(6,7)$. How do I ...