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Question

# MATCHI THE FOLLOWINGA point 'z' moves on the |z−5i|+|z−11i|=10 then match the following column. Column I Column II1. Maximum |z| (p) 32. Minimum |z| (q) √3943.tan(minargz) (r) 134.tan(maxargz) (s) 10+√394

A
1r
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B
2p
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C
3q
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D
4q
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Solution

## The correct options are A 3→q B 2→p C 1→r D 4→q|z−5i|+|z−11i|=10⇒S′=(0,11),S=(0,5),C=(0,8)Here 2a=10⇒a=5Now 2ae=SS′=6 ⇒ae=3,a=5⇒e=35Now b2=a2(1−e2)=16⇒b=4Maximum of |z|=13Minimum of |z|=3Equation of the ellipse is x216+(y−8)225=1 ...(1)Equation of the line passing through the argin is y=mx ...(2)From (1) and (2) x2m2(16)+(y−8)225=1⇒y2(25+16m2)−(16)2m2y+16m2(39)=0(1) and (2) ratisfed by same ′y′ values ∴△=0⇒m=±√394∴|tan(min(asgz))|=√394∴|tan(max(asgz))|=√394

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