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Sep 12, 2020 · Two curves are parallel if at any point you draw a line perpendicular to the tangent line and passes through the point of tangency (the normal line), the normal lines are all parallel, at any point along the curve, and the distance between the line's points of intersections with the two curves are all the same.
- calculus - Parallel functions. - Mathematics Stack Exchange
You are looking for the parallel curves to a given curve....
- calculus - Parallel functions. - Mathematics Stack Exchange
- Overview
- Comparing the Slopes of Each Line
- Using the Slope-Intercept Formula
- Defining a Parallel Line with the Point-Slope Equation
Parallel lines are two lines in a plane that will never intersect (meaning they will continue on forever without ever touching).
A key feature of parallel lines is that they have identical slopes.
The slope of a line is defined as the rise (change in Y coordinates) over the run (change in X coordinates) of a line, in other words how steep the line is.
Parallel lines are most commonly represented by two vertical lines (ll). For example, ABllCD indicates that line AB is parallel to CD.
Define the formula for slope.
The slope of a line is defined by (Y
) where X and Y are the horizontal and vertical coordinates of points on the line. You must define two points on the line to calculate this formula. The point closer to the bottom of the line is (X
) and the point higher on the line, above the first point, is (X
This formula can be restated as the rise over the run. It is the change in vertical difference over the change in horizontal difference, or the steepness of the line.
If a line points upwards to the right, it will have a positive slope.
Define the slope-intercept formula of a line.
The formula of a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. In this form, you can easily determine the slope of the line as the variable "m".
For example. Rewrite 4y - 12x = 20 and y = 3x -1. The equation 4y - 12x = 20 needs to be rewritten with algebra while y = 3x -1 is already in slope-intercept form and does not need to be rearranged.
Rewrite the formula of the line in slope-intercept form.
Oftentimes, the formula of the line you are given will not be in slope-intercept form. It only takes a little math and rearranging of variables to get it into slope-intercept.
For example: Rewrite line 4y-12x=20 into slope-intercept form.
Point-slope form allows you to write the equation of a line when you know its slope and have an (x, y) coordinate. You would use this formula when you want to define a second parallel line to an already given line with a defined slope. The formula is y – y
= m (x – x
) where m is the slope of the line, x
is the x coordinate of a point given on the line and y
is the y coordinate of that point.
As in the slope-intercept equation, x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation.
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Parallel Lines. How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2.
- Slope
- −0.5
DescriptionIn this video you will learn about parallel curve in geometry including their definitions and where we can find them in real life.This video seri...
- 3 min
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- Sinny's Primary Math
Two definitions of a parallel curve: 1) envelope of a family of congruent circles, 2) by a fixed normal distance. The parallel curves of a circle (red) are circles, too. A parallel of a curve is the envelope of a family of congruent circles centered on the curve. It generalises the concept of parallel (straight) lines.
You found that $x=-3$ or $x=1$, so there are two points on the curve where the tangent is parallel to the line $x-2y=2$; one is $(-3,2)$, and the other is $(1,0)$. Now you just find the tangent lines to $y=\frac{x-1}{x+1}$ at those two points.
You are looking for the parallel curves to a given curve. The link shows you how to obtain these curves for curves given parametrically.
