deduce the equation

[pipe]

hello guys, again me and the ellipses ... jajajajaja
i only have this:
the sum of 2 distances to the each point to the points (5;3) and (4;-2) is 6
deduce the equation of the ellipse


so i got this...
the sum of the distances are the distance between the axis of the ellipse so the distance from the focus1 to the center is $\displaystyle \displaystyle{ \frac{sqrt(26)}{2}}$
i got his using the distance formule, so I deduct $\displaystyle \displaystyle{ \frac{sqrt(26)}{2}}$ this from the first point (5;3) and that's mi center.
so i don't know how to find the distance between the center and the axis parallel to the x-axis and y-axis.
thank you very much for the help.


P.D: (sorry for the writing, i'm learning )

 

[pka]

hello guys, again me and the ellipses
i only have this:
the sum of 2 distances to the each point to the points (5;3) and (4;-2) is 6
deduce the equation of the ellipse

$\displaystyle \sqrt{(x-5)^2+(y-3)^2}+\sqrt{(x-4)^2+(y+2)^2}=6$

 

[HallsofIvy]

hello guys, again me and the ellipses ... jajajajaja
i only have this:
the sum of 2 distances to the each point to the points (5;3) and (4;-2) is 6

So (5, 3) and (4, -2) are the foci of the ellipse.

deduce the equation of the ellipse


so i got this...
the sum of the distances are the distance between the axis of the ellipse so the distance from the focus1 to the center is $\displaystyle \displaystyle{ \frac{sqrt(26)}{2}}$
i got his using the distance formule, so I deduct $\displaystyle \displaystyle{ \frac{sqrt(26)}{2}}$ this from the first point (5;3) and that's mi center.

No, the center is half way between the two foci: (9/2, 1/2).

so i don't know how to find the distance between the center and the axis parallel to the x-axis and y-axis.

There are NO "axes parallel to the x-axis and y-axis". The major axis is the line through the two given foci. y= 5(x- 5)+ 3. The minor axis is the line through (9/2, 1/2) perpendicular to that:
y= (-1/5)(x- 9/2)+ 1/2.

thank you very much for the help.

P.D: (sorry for the writing, i'm learning )

 

[pipe]

So (5, 3) and (4, -2) are the foci of the ellipse.


No, the center is half way between the two foci: (9/2, 1/2).


There are NO "axes parallel to the x-axis and y-axis". The major axis is the line through the two given foci. y= 5(x- 5)+ 3. The minor axis is the line through (9/2, 1/2) perpendicular to that:
y= (-1/5)(x- 9/2)+ 1/2.

thank you have a nice day.