Finding the coordinates of endpoints

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In summary, to find the coordinates of the endpoints of the major axis for an equation of an ellipse, first find the center of the ellipse and the lengths of the semi-axes in the x and y directions. Then, the endpoints of the major axis can be determined by adding and subtracting the semi-axis lengths from the center coordinates in each direction.
  • #1
trigger352
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How do you find the coordinates of endpoints of the major axis for an equation like

[tex]\frac{(x-1)^2}{16} + \frac{(y+2)^2}{25} = 1[/tex]

I'm just trying to develop the tequnique here. What should I be looking for? What numbers are important to an equation like this...
 
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  • #2
I like to help you out but i can't really understand your question...are you trying to say by the "endpoints" as in the y and x values. If you could clarify your question i might be able to help you...

take care,
aek
 
  • #3
Yeah, like...a pair of points. (x,y);(x,y)
 
  • #4
Hint:
find the center (h,k) first...
the major axis is a line horizontally or vertically passes through the eclipse, depend on which one is longer...
you should able to figure out the rest...
 
  • #5
In your example, the center of the ellipse is at (1, -2) and the semi-axis in the x direction is 4 so the endpoints of the axis of the ellipse, in the x direction, are (1+4,-2)= (5,-2) and (1-4,-2)= (-3,-2). The semi-axis in the y direction is 5 so the endpoints of the axis of the ellipse, in the y direction, are (1,-2+5)= (1, 3) and (1, -2-5)= (1, -7)
 

1. How do I find the coordinates of the endpoints on a line segment?

The coordinates of the endpoints on a line segment can be found by identifying the two points where the line segment meets the x-axis and y-axis. These points are typically denoted as (x1, y1) and (x2, y2), where x1 and x2 represent the x-coordinates and y1 and y2 represent the y-coordinates.

2. What is the formula for finding the coordinates of the endpoints?

The formula for finding the coordinates of the endpoints on a line segment is (x1, y1) and (x2, y2), where x1 and y1 represent the coordinates of the first endpoint and x2 and y2 represent the coordinates of the second endpoint.

3. Can I find the coordinates of the endpoints on a curved line?

No, the concept of endpoints only applies to straight lines. Curved lines have infinite points and do not have distinct endpoints.

4. How do I use a graph to find the coordinates of the endpoints?

To use a graph to find the coordinates of the endpoints, plot the line segment on the graph and identify the points where the line segment meets the x-axis and y-axis. These points will represent the coordinates of the endpoints.

5. What is the importance of finding the coordinates of the endpoints?

Finding the coordinates of the endpoints is important in geometry and mathematics as it helps to accurately describe and measure line segments. It also allows for the calculation of distance, slope, and other important properties of a line segment.

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