2+4) n z is represented by a point ...
Question

# 2+4) n z is represented by a point 54. If Re- 22-1) lying on (1) A circle 0=20 - Bler (2) An ellipse (3) A straight line (4) No real locus 0-

JEE/Engineering Exams
Maths
Solution
58
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( operatorname{Re}left(frac{z+4}{g z-1}right)=frac{1}{2}, quad underbrace{sum_{D A T E: N_{0}} 120} ) ( log x=x+1 y ) The ( quad ) Re ( left[frac{x+(y+4)}{2(x+i y)-1}right]=frac{1}{2} ) ( R eleft[frac{x+4+i y}{(2 x-1)+(2 y)}right]=frac{1}{2} ) ( R eleft[frac{(x+4)+(y)}{(2 x-1+2(2 y)} times frac{(2 x-1)-12 y)}{(2 x-1)-(2 y)}right]=frac{1}{2} ) ( operatorname{Ro}left(frac{x+4)(2 x+1)+y(2 y)}{(2 x-1)^{2}+(2 y) 2}right]=frac{1}{2} ) e ( left[x^{x}right)^{2}+x-4 ) 7 ( 2 x y x^{2}-y x ) ( 2left(2 x^{2}+y x-y+2 yright)=4 x^{2}-4 y^{2} ) ( 4 x^{2}+y 4 x-2+2 y^{2}-4 x^{2}-4 y^{2}-4 x+1 ) ( 4 y^{2}+8 y+18 x-1=0 ) ( frac{2 x^{2}+7 x-4+2 y^{2}}{4 x^{2}-4 x+1+4 y^{2}}=frac{1}{2} ) ( 42 x^{2}+14 x-8+y+2=y x^{2}-4 x+1+y x^{2} ) ( 18 x=9 ) ( C ) ( mid x=1 / 2 ) Qu orsing hr Give your feedback