Question 1077945
an ellipse with foci {{{F[1]}}} ({{{3}}},{{{ 0}}}), {{{F[2]}}} ({{{24}}}, {{{0}}}) and the point on the ellipse ({{{9}}}, {{{8}}})

One property of an ellipse is that, from any point, the sum of the {{{distances}}} to the two foci is {{{constant}}}.

{{{sqrt((9-3)^2+(8-0)^2)+sqrt((9-24)^2+(8-0)^2)}}}

{{{sqrt((6)^2+(8)^2)+sqrt((-15)^2+(8)^2)}}}

{{{sqrt(36+64)+sqrt(225+64)}}}

{{{sqrt(100)+sqrt(289)}}}

{{{10+17}}}

{{{27}}}

The constant sum is: __{{{27}}}___.