Analytic geom: Find lengths of chords of 4x^2 + y^2 = 36

[Kanimoto]

I don't need help solving the problem; I just need an explanation.

Find the length of the chords joining the points of intersection of 4x^2 + y^2 = 36 with a) x=1; b) x=-2; c) y=1; d) y=-1.

I know that 4x^2 + y^2 = 36 is an ellipse, but do they just want me to draw chords from where a-d intersect the ellipse? Is that all I need to do to find their length? Thanks.

 

[soroban]

Re: Analytic geometry help

Hello, Kanimoto!

Find the length of the chords joining the points of intersection of \(\displaystyle \,4x^2\,+\,y^2 \:= \:36\)

with \(\displaystyle \:\begin{array}{cccc}a) & x\:=\:1\\b) & x\,=\,-2 \\ c) & y\:=\:1\\ d) & y\,=\,-1\end{array}\)


I know that \(\displaystyle 4x^2\,+\,y^2\:=\:36\) is an ellipse. . Good!
But do they just want me to draw chords from where a-d intersect the ellipse?
Is that all I need to do to find their length? . You still have to determine their lengths.

\(\displaystyle a)\:x\,=\,1\)

The equation becomes: \(\displaystyle \:4(1^2)\,+\,y^2\:=\:36\;\;\Rightarrow\;\;y^2\,=\,32\;\;\Rightarrow\;\;y\,=\,\pm4\sqrt{2}\)

The ends of the chord are: \(\displaystyle \,(1,\,-4\sqrt{2})\) and \(\displaystyle (1,\,4\sqrt{2})\)

                  |
                * * *             _
          *       |       * (1, 4√2)
        *         |       : *
       *          |       :  *
                  |       :
      *           |       :   *
  ----*-----------+-------+---*----
      *           |       :   *
                  |       :
       *          |       :  *
        *         |       : *     _
          *       |       * (1,-4√2)
                * * *
                  |

You don't need the Distance Formula, do you?

 

[Kanimoto]

No, I already know the distance formula. Thanks, that helps a lot!