Posted by Jamie on Thursday, April 8, 2010 at 7:35pm.
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, Thursday, April 8, 2010 at 9:21pm
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, Thursday, April 8, 2010 at 9:46pm
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, Thursday, April 8, 2010 at 10:03pm
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, Thursday, April 8, 2010 at 10:30pm
Thanks, but where did you get the
2a = 10
from?

calculus  Reiny, Thursday, April 8, 2010 at 10:42pm
by definition, the sum of the two focal length is 2a
check, distance from centre to the x vertex is a + a = 2a
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