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what is the general equation if the locus of a point which moves so that the sum of its distances from point (2,1) and (8,1) is 10?
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This locus is an ellipse with the foci at the points (2,1) and (8,1);
the major axis is directed along (parallel to) x- axis;
The center is at the point (5,1);
the focal distance is 8-2 = 6;
the linear eccentricity "c" is = 3 units (c=3);
the minor semi-axis "b" is = = 4 (b=4); ( <--- here 5 = )
the major semi-axis "a" is = = = 5 units long.
The equation of this ellipse is
+ = 1.
See the lessons on ellipses
- Ellipse definition, canonical equation, characteristic points and elements
- Ellipse focal property
- Tangent lines and normal vectors to a circle
- Tangent lines and normal vectors to an ellipse
- Optical property of an ellipse
- Optical property of an ellipse revisited
in this site.