Write the standard equation of each Ellipse. Find the center, vertices, co-vertices and foci.

1. 25x2 + 9y2 = 225

2. 49x2 + y2 = 49

3. x2 - 2x + 9y2 - 8 = 0

4. x2 + 4y2 - 18x -8y + 81 = 0

Question

Write the standard equation of each Ellipse. Find the center, vertices, co-vertices and foci.
 
1. 25x2 + 9y2  = 225
 
2. 49x2 + y2 = 49
 
3. x2 - 2x + 9y2 - 8 = 0
 
4. x2 + 4y2 - 18x -8y + 81 = 0

anonymous · Answer

Familiar with 'completing-the-square?'

anonymous · Answer

no

anonymous · Answer

Ok, we can review that. There is an equivalent way to do the same thing that might be easier, so I'll show you that too. You'll only need that for #3 and #4; the first two can be solved immediately.

anonymous · Answer

ok thanks

anonymous · Answer

The standard form for an ellipse looks like this.
$$\large \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$$

anonymous · Answer

ok

anonymous · Answer

The center is at (h,k) and a and b are the semi-axes.
Look at #1 and see what you have to do to put it into standard form.

anonymous · Answer

. 25x2 + 9y2  = 225

anonymous · Answer

It needs to be set equal to 1, so what's the easy step that will take care of that?

anonymous · Answer

So that's all you have to do for #1 and #2; let me know when you are ready to move on to the last two.