how abot this question:
The locus of points the sum of whose distances from the points (1,0) and (-1,0) equals 2.
What is the locus of points and how is the distance?
Hi sandy,
Square both sides
is common
is common
Square both sides
The only way these can be equal is if y=0.
You should note that you can see the solution geometrically,
by just following mr fantastic's hint.
The distance from (-1,0) to (1,0) is 1-(-1)=2.
The shortest distance between 2 points is a straight line.
Hence any point not between (-1,0) and (1,0) must be a combined distance >2 from those two points.
Any point between (-1,0) and (1,0) is a combined distance of 2 from the two points.
Visually, placing any point above the line segment, you can see that the
combined hypotenuses of the two right-angled triangles formed
have sum of lengths > the combined lengths of the bases.
Hence, any point not on the line segment is more than 2 combined units from those points.