Complex Numbers
Circle from Modulus Ratio — Centre and Radius
nta_pyq_2023_jan
Grade 11
Question:
If the centre and radius of the circle $\left|\dfrac{z-2}{z-3}\right|=2$ are respectively $(\alpha,\beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to:
Step-by-Step Solution
Key Concept: $|z-2|^2=4|z-3|^2$. $(x-2)^2+y^2=4((x-3)^2+y^2)$. $3x^2+3y^2-20x+32=0\Rightarrow x^2+y^2-\frac{20}{3}x+\frac{32}{3}=0$.
$3(\alpha+\beta+\gamma)=12$.
Correct Answer: 4