I Need Help With Ellipses!!! And Conics!!!

**blueskiiiedchica** · June 15th 2008, 06:36 PM

Hi. I'm in a panic, because i have this take home quiz i need to do for class, and I'm pretty lost when it comes to algebra II.

The homework says that I need to scetch the ellipse whose foci are (1,4) and (1,2)
and whose minor axis is 8 units, then i have to write the equation of that ellipse.

also i need to, from standard form, classify each conic, the identify its center:

1. (x+6)^2 ---(y-5)^2
________ + _________= 1
------- 81 - - - - - 64

2. x^2+8y^2-4x-16y-4=0

3. x^2+y^2+6x+6y=0

And of course, I forgot my textbook in my locker, and I've searched all over the web, but am still having trouble understanding this stuff. Someone please help me.

-Tessa

**mr fantastic** · June 15th 2008, 07:43 PM

Originally Posted by blueskiiiedchica

[snip]
i need to, from standard form, classify each conic, the identify its center:

1. (x+6)^2 ---(y-5)^2
________ + _________= 1
------- 81 - - - - - 64

2. x^2+8y^2-4x-16y-4=0

3. x^2+y^2+6x+6y=0

And of course, I forgot my textbook in my locker, and I've searched all over the web, but am still having trouble understanding this stuff. Someone please help me.

-Tessa

How long have you had to prepare for this take-home quiz. You need to do a bit more work and get better organised.

Standard form of ellipse with centre at (h, k): $\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$ .

1. See above.

2 and 3. Complete the square in x and y and re-arrange into above standard form.

Eg. $x^2 + 6y^2 - 4x + 12y - 15 = 0 \Rightarrow (x^2 - 4x) + (6y^2 + 12 y) - 15 = 0$

$\Rightarrow (x - 2)^2 - 4 + 6 (y^2 + 2y) - 15 = 0 \Rightarrow (x - 2)^2 - 4 + 6[(y + 1)^2 - 1] - 15 = 0$

$\Rightarrow (x - 2)^2 - 4 + 6(y + 1)^2 - 6 - 15 = 0 \Rightarrow (x - 2)^2 - 4 + 6[(y + 1)^2 - 1] - 15 = 0$

$\Rightarrow (x - 2)^2 - 4 + 6(y + 1)^2 - 6 - 15 = 0 \Rightarrow (x - 2)^2 + 6(y + 1)^2 = 25$

$\Rightarrow \frac{(x - 2)^2}{25} + \frac{6(y + 1)^2}{25} = 1$ etc.

**blueskiiiedchica** · June 15th 2008, 07:59 PM

Oh, thank you so much! I've been scratching my head over this for hours. Yes, usually I would prepare better, but I've had bronchitis and have been a mess =[

**mr fantastic** · June 15th 2008, 08:01 PM

Originally Posted by blueskiiiedchica

Hi. I'm in a panic, because i have this take home quiz i need to do for class, and I'm pretty lost when it comes to algebra II.

The homework says that I need to scetch the ellipse whose foci are (1,4) and (1,2)
and whose minor axis is 8 units, then i have to write the equation of that ellipse.

[snip]

Label the focii on a set of axes. You should be able to draw a rough ellipse around them.

You know the centre is half-way between the focii, right? So you can get h and k.

And you know that the focii lie on the major axis, which in the case is parallel to the y-axis. So the minor axis is parallel to the x-axis. Therefore length of minor axis is 2a = 8 => a = 4.

Use your diagram and Pythagoras' Theorem to see why $b = \sqrt{17}$ .

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