Posted by Jamie on .
Find the equation of the following. The locus of all points in a plane such that the sum of the distances from points (2,1) and (10,1) is equal to 6.

calculus 
Reiny,
I think you have an impossible situation
the distance between the two given points is 8 units
The sum of the distance from any point to the two given points has to be greater than 8 
calculus 
Jamie,
Oh shoot. You're right. I took the last part from a different problem. The sum of the distances is equal to 10. Sorry.

calculus 
Reiny,
Now it becomes an ellipse.
from the data
2a = 10
a = 5
the two given points are the foci
and the centre would have to be the midpoint of those, namely
(6.1)
the distance form the centre to one focal point is the c value, here it would be 4
In an ellipse with the a horizontal major axis
b^2 + c^2 = a^2
b^2 + 16 = 25
b = 3
in standard form then
(x+6)^2/25 + (y+1)^2/9 = 1 
calculus 
Jamie,
Thanks, but where did you get the
2a = 10
from? 
calculus 
Reiny,
by definition, the sum of the two focal length is 2a
check, distance from centre to the x vertex is a + a = 2a