If the equation $\mathrm{a}|\mathrm{z}|^{2}+\overline{\bar{\alpha}_{\mathrm{Z}}+\alpha \overline{\mathrm{z}}}+\mathrm{d}=0$ represents a circle where $\mathrm{a}, \mathrm{d}$ are real constants then which of the following condition is correct?
Correct Option: , 2
$\mathrm{az} \overline{\mathrm{z}}+\alpha \overline{\mathrm{z}}+\bar{\alpha} \mathrm{z}+\mathrm{d}=0 \rightarrow$ Circle
centre $=\frac{-\alpha}{\mathrm{a}} \quad 2=\sqrt{\frac{\alpha \bar{\alpha}}{\mathrm{a}^{2}}-\frac{\mathrm{d}}{\mathrm{a}}}=\sqrt{\frac{\alpha \bar{\alpha}-\mathrm{ad}}{\mathrm{a}^{2}}}$
So $|\alpha|^{2}-\mathrm{ad}>0 \& \mathrm{a} \in \mathrm{R}-\{0\}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.