Question

The locus of z such that $\frac{|z-i|}{|z+i|}$= 2, where z = x+iy. is

• A. 3x2 + 3y2 +10y + 3
• B. 3x2 - 3y2 - 10y - 3 = 0
• C. 3x2 + 3y2 + 10y + 3 = 0
• D. x2 + y2 - 5y + 3 = 0

Answer 1

Answer: (C)

3x2 + 3y2 + 10y + 3 = 0

Answer 2

The correct option is: (A): 3x2 + 3y2 + 10y + 3 = 0.

Given: ∣ z − i ∣=2∣ z +i ∣

Hence: ∣​2 z − i ​∣∣​2=∣∣​1 z +i ​∣∣​2

This simplifies to: x 2+(y −1)2=4(x 2+(y +1)2)

Further simplifying: 3 x 2+4(y +1)2−(y −1)2=0

And: 3 x 2+3 y 2+8 y +2 y +4−1=0

Finally: 3x2 + 3y2 + 10y + 3 = 0.