Parametric line intersecting with x and y axis

Thread starter azn4lyf89
Start date Sep 4, 2008
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Axis Line Parametric

In summary, a parametric line is a mathematical representation of a line using parameters x and y. It intersects with the x and y axis when the values of x and y satisfy the equations of the line, and the x and y intercepts provide information about the slope and direction. The x and y intercepts can be found by setting y=0 and x=0 respectively. A parametric line can intersect with the x and y axis at more than one point, depending on the slope of the line.

Sep 4, 2008

azn4lyf89

Consider the line L(t)=<4t-1,2+2t>. Then L intersects:
1. the x-axis at point ____ when t=____
2. the y-axis at point ____ when t=____
3. the parabola y=x^2 at the points _____ and _____ when t=_____ and t=______

I am confused on how to approach this problem. Do I just make x=4t-1 and y=2+2t?

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Sep 4, 2008

Dick

Science Advisor

Homework Helper

Yes. Exactly.

What is a parametric line?

A parametric line is a mathematical representation of a line using parameters, typically denoted by the variables x and y. It allows for a more flexible and versatile way of representing a line in two-dimensional space.

How does a parametric line intersect with the x and y axis?

A parametric line intersects with the x and y axis when the values of x and y satisfy the equations of the line. In other words, the parametric line will have a point of intersection with the x and y axis at the coordinates (x,y).

What is the significance of the x and y intercepts in a parametric line?

The x and y intercepts in a parametric line represent the points where the line intersects with the x and y axis, respectively. They can provide valuable information about the slope and direction of the line.

How do you find the x and y intercepts of a parametric line?

The x intercept can be found by setting y=0 in the parametric equations and solving for x. Similarly, the y intercept can be found by setting x=0 and solving for y.

Can a parametric line intersect with the x and y axis at more than one point?

Yes, a parametric line can intersect with the x and y axis at more than one point as long as the values of x and y satisfy the equations of the line. This can happen when the line is not perfectly horizontal or vertical.