Grade 12Analytical Geometry
if | z – 4 | + | z – [12/5] | = 10 represents an ellipse , then what is its eccentricity?
if | z – 4 | + | z – [12/5] | = 10
represents an ellipse , then what is its eccentricity?
1 Answer
Riddhish Bhalodia
I am assuming that [12/5] is the greatest integer function, which will change the equation to
|z-4| + |z-2| = 10
Now Interpreting this as an ellipse is simple, basically the equation can be interpreted as the locus of a point in complex plane whose sum of distance from the points (4,0) and (2,0) is 10. This is the definition of an ellipse with focii as (4,0) and (2,0) and
2a = 10 thus a = 5 (semi-major axis). And distance between focii is 2ae = 2 adn hence
e = 1/a = 1/5
|z-4| + |z-2| = 10
Now Interpreting this as an ellipse is simple, basically the equation can be interpreted as the locus of a point in complex plane whose sum of distance from the points (4,0) and (2,0) is 10. This is the definition of an ellipse with focii as (4,0) and (2,0) and
2a = 10 thus a = 5 (semi-major axis). And distance between focii is 2ae = 2 adn hence
e = 1/a = 1/5
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