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- Parallel lines have the same slope. Because the functions each have a slope of 2, they represent parallel lines. Perpendicular lines have negative reciprocal slopes. Because −2 and are negative reciprocals, the equations, represent perpendicular lines.
courses.lumenlearning.com/waymakercollegealgebra/chapter/parallel-and-perpendicular-lines-2/
How do you find parametric equations and symmetric equations for the line through #(3, −2, 5)# and parallel to the line #x + 3 = y/2 = z − 2#? How do you show that the curve x=cos t , y= sin t cos t has two tangents at (0,0) and find their equations?
- X = T
Write t as a function of x then substitute that function...
- Theta
How do you sketch the curve with parametric equations #x =...
- 1 and Y = T^3
How do you sketch the curve with parametric equations #x =...
- Y = 2 + X
parametrising a straight line is a bit of a waste of time...
- X = T
Dec 29, 2020 · If a curve is not smooth at \(t=t_0\), it means that \(x^\prime(t_0)=y^{\prime}(t_0)=0\) as defined. This, in turn, means that rate of change of \(x\) (and \(y\)) is 0; that is, at that instant, neither \(x\) nor \(y\) is changing. If the parametric equations describe the path of some object, this means the object is at rest at \(t_0\).
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.
Aug 15, 2023 · We know a point on the line and just need a parallel vector. We know that the new line must be parallel to the line given by the parametric equations in the problem statement. That means that any vector that is parallel to the given line must also be parallel to the new line.
Jul 5, 2023 · In this section we will introduce parametric equations and parametric curves (i.e. graphs of parametric equations). We will graph several sets of parametric equations and discuss how to eliminate the parameter to get an algebraic equation which will often help with the graphing process.
The graph of parametric equations is called a parametric curve or plane curve, and is denoted by [latex]C[/latex]. Notice in this definition that [latex]x[/latex] and [latex]y[/latex] are used in two ways.
Find the equations of parallel and perpendicular lines. Write the equations of lines that are parallel or perpendicular to a given line. Parallel lines have the same slope and different y- intercepts.
