Question

Match the statements of Column I with those of Column II. Here, z takes values in the complex plane and Im (2) and Re (2) denote respectively, the imaginary part and the real part of 2 (2010) Column Il A. p. an ellipse with eccentricity 4/5 B. Column ! The set of points z satisfying 12-il zll=12+ ilzil is contained in or equal to The set of points z satisfying 12+ 4 + 1 Z-4)= 0 is contained in or equal to If|w1=2, then the set of points z = w+ -is contained q. the set of points z satisfying Im (z) = 0 C. the set of points z satisfying|Im(z) |31 w D. in or equal to if w/= 1, then the set of points s. Z=w+ - is contained in ort W the set of points satisfying Re(z) < 2 the set of points z satisfying|zl s 3 equal to

JEE/Engineering Exams

Maths

Solution

155

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Ans: ( (A)-(q),(r) ;(B)-(p) ;(C)-(p),(s),(t) ;(D)-(q),(r),(s),(t) ) Sol: ( (A)-(q),(r) ;(B)-(p) ;(C)-(p),(s),(t) ;(D)-(q),(r),(s),(t) ) ( z ) is pureb real ( a ) ( Rightarrow operatorname{Im} z=0 ) b. ( z ) is on ellipse ( frac{x^{2}}{25}+frac{y^{2}}{9}=1 ) ( z=frac{3}{2} cos theta+frac{5}{2} i sin theta Rightarrow frac{3}{2} leq|z| leq frac{5}{2} ) Also represents ellipse( frac{4 x^{2}}{9}+frac{4 y^{2}}{25}=1 ) whose eccentricity ( =frac{4}{5} ) d. ( z=2 cos theta )