KVPY 2020-21 SB SX Exam Previous Papers

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Question : 20 of 120

Marks: +1, -0

The figure in the complex plane given by

10 {z} \ov {{z}}-3({z}^{2}+\ov {{z}}^{2})+4 {i}({z}^{2}-\ov {{z}}^{2})=0

is

a straight line
a circle
a parabola
an ellipse

Solution:

10 {z} \ov {{z}}-3({z}^{2}+\ov {{z}}^{2})+4 {i}({z}^{2}-\ov {{z}}^{2})=0

Let

z=x+i y

10(x^{2}+y^{2})-3(4 x^{2}-2 x^{2}-2 y^{2})

+4 i(2 x(2 i y))=0

\⇒4 x^{2}+16 y^{2}-16 x y=0

\⇒x^{2}-4 x y+4 y^{2}=0

\⇒(x-2 y)^{2}=0 \⇒x=2 y

\∴

straight line

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