Word Problem

[vanbeersj]

The circle x^2+y^2+4x-5=0 passes through the foci and the ends of the minor axis of an ellipse that has its major axis along the x-axis. Find the equation of the ellipse.

So i took the equation and completed the square and I ended up with (x+2)^2 + y^2=9, if I divide this through I get

(x+2)^2/9 +y^2/9=1

I'm not sure if I did this correctly as I'm left with the y^2. Please help.

 

[soroban]

Hello, vanbeersj!

The circle \(\displaystyle x^2+y^2+4x-5\:=\:0\) passes through the foci and the ends of the minor axis
of an ellipse that has its major axis along the \(\displaystyle x\)-axis. .Find the equation of the ellipse.

\(\displaystyle \text{The circle is: }\x+2)^2 + y^2 \:=\:9\)

\(\displaystyle \text{Its center is: }\:C(-2,0)\text{ and its radius is }3.\)

                              |
                ...   * o *   |...
           ..*::::*     :     *::::*..
          *:::::*       :     | *:::::* 
        *::::::*        :3    |  *::::::*
       *::::::'         :     |  ':':::::*
      *:::::::*F'     -C:     |  F*:::::::*
  . . *:-:-:-:o - - - - o - - + - o:-:-:-"* - -
      *:::::::*-5      -2     |  1*:::::::*
       *::::::,         :     |   ,::::::*
        *::::::*        :3    |  *::::::*
          *:::::*       :     | *:::::* 
             *::::*     :     *::::*
                      * o *   |
                              |

\(\displaystyle \text{For the ellipse, the foci are at: }\:F(1,0),\:F'(-5,1) \quad\hdots\;\;c = 3\)
\(\displaystyle \text{It has the same center: }\:C(-2,0)\)
\(\displaystyle \text{The semiminor axis is: }\:b = 3\)
. . \(\displaystyle \text{Hence: }\:a^2 \:=\:a^2+b^2 \:=\:3^2 + 3^2 \:=\:18\)

\(\displaystyle \text{The equation of the ellipse is: }\;\frac{(x+2)^2}{18} + \frac{y^2}{9} \;=\;1\)

 

[galactus]

Whoa...do I feel stupid. I completely flubbed that up. I am deleting it forewith. Thanks Soroban for pointing my idiocy.

My technique was sound, but I screwed up in the algebra. Bad Cody :evil: