JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q63

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MathematicsSingle correct+4 / -1Question 63 of 90

Let $z\in\mathbb C$ , the set of complex numbers. Then the equation, $2|z+3i|-|z-i|=0$ represents :

a circle with radius

\dfrac83

a circle with diameter

\dfrac{10}3

an ellipse with length of major axis

\dfrac{16}3

an ellipse with length of minor axis

\dfrac{16}9

Answer and worked solution

Official answer: A

With $z=x+iy$ , $4\left(x^2+(y+3)^2\right)=x^2+(y-1)^2$ , i.e.
$x^2+y^2+\frac{26}3y+\frac{35}3=0.$
The centre is $\left(0,-\frac{13}3\right)$ and $r^2=\frac{169}9-\frac{105}9=\frac{64}9$ : a circle of radius $\frac83$ .

Topics:Geometry in the complex plane Equation of a circle

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JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 63