Finding the coordinates of endpoints

[trigger352]

How do you find the coordinates of endpoints of the major axis for an equation like

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

I'm just trying to develop the tequnique here. What should I be looking for? What numbers are important to an equation like this...

 

[aek]

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

 

[trigger352]

Yeah, like...a pair of points. (x,y);(x,y)

 

[vincentchan]

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...

 

[HallsofIvy]

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)