MCQ
$\alpha, \beta, z \in C$ અને $\lambda>1$ માટે ,જો $\sqrt{\lambda-1}$ એ વર્તુળ $|z-\alpha|^2+|z-\beta|^2=2 \lambda$ ની ત્રિજ્યા છે તો $|\alpha-\beta|$ ની કિમંત $.............$ મેળવો.
- A$4$
- B$6$
- C$2$
- D$8$
$\left|z-z_1\right|^2+\left|z-z_2\right|^2=\left|z_1-z_2\right|^2$
$r =\frac{\left|z_1-z_2\right|}{2}=\frac{|\alpha-\beta|}{2}=\sqrt{\lambda-1}$
$2 \lambda=|\alpha-\beta|^2$
$|\alpha-\beta|=2 \sqrt{\lambda-1}$
$|\alpha-\beta|^2=4 \lambda-4=2 \lambda$
$\lambda=2$
$\Rightarrow|\alpha-\beta|^2=4$
$|\alpha-\beta|=2$
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