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Question
If |z−z1|+|z−z2|=k(>|z1−z2|), then the locus of z is a/an:
(Given: z1 and z2 are fixed complex numbers)
If |z−z1|+|z−z2|=k(>|z1−z2|), then the locus of z is a/an:
(Given: z1 and z2 are fixed complex numbers)
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Solution
The correct option is B ellipse
|z−z1| is the distance of 'z' from 'z1'
|z−z2| is the distance of 'z' from 'z2'
→ Thus |z−z1|+|z−z2|=k(>|z1−z2|) represents the locus of point whose distance from the two points 'z1' & 'z2' is constant i.e. ′k′
→ This is exactly the defination of ellipse which says that the sum of distances of any point on the ellipse from the focii is constant & is equal to '2a'. (major axis of ellipse).
'z1' & 'z2' are the two focii of the ellipse
|z−z1| is the distance of 'z' from 'z1'
|z−z2| is the distance of 'z' from 'z2'
→ Thus |z−z1|+|z−z2|=k(>|z1−z2|) represents the locus of point whose distance from the two points 'z1' & 'z2' is constant i.e. ′k′
→ This is exactly the defination of ellipse which says that the sum of distances of any point on the ellipse from the focii is constant & is equal to '2a'. (major axis of ellipse).
'z1' & 'z2' are the two focii of the ellipse
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