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

## Answer this Question

## Related Questions

- Geometry - How many points in a plane are in the locus of all points ...
- Geo (locus) - I don't fully get this stuff but some of these I guessed on and ...
- math - what is the locus of the midpoints of the line segments joining a given ...
- algebra 2 - Find the equation that is satisfied by the set of points such that ...
- Math - Find the equation of the graph of all points such that the difference of...
- Reply to grant about a regression problem - This is a reply to the question ...
- Physics - A train travels between stations 1 and 2. The engineer of the train is...
- Calc - "Consider the surface given by 4x^2-y^2+5z^2-10z=55. a) Find all points ...
- Math - Find the locus of points that satisfy (a) |z+1| = |z+i| (b) Re z = |z-1| ...
- Calculus - Find the scalar equation of the plane through the points M(1,2,3) and...