For all complex numbers $z_{1}, z_{2}$ satisfying $| z_{1} | = 12 a n d | z_{2} - 3 - 4 i |$ = 5, the minimum value of $| z_{1} - z_{2} |$ is
[IIT Screening 2002]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
2

The two circles are $C_{1} (0, 0), r_{1} = 12, C_{2} (3, 4), r_{2} = 5$ and it passes through origin, the centre of $C_{1}$ .
$C_{1} C_{2} = 5 < r_{1} - r_{2} = 7$

Hence circle $C_{2}$ lies inside circle $C_{1}$ .
Therefore minimum distance between them is $A B = C_{1} B = C_{1} A = r_{1} - 2 r_{2} = 12 - 10 = 2.$

Suggest Corrections

Similar questions

z_{1}, z_{2}

| z_{1} | = 12 a n d | z_{2} - 3 - 4 i |

| z_{1} - z_{2} |

For all complex numbers $Z_{1}, Z_{2}$ satisfying | $Z_{1}$ | = 12 and | $Z_{2} - 3 - 4 i |$ = 5 , the minimum value of | $Z_{1} - Z_{2}$ | is

z_{1}, z_{2}

| z_{1} |

| z_{2} - 3 - 4 i | = 5

| z_{1} - z_{2} |

z_{1}, z_{2}

| z_{1} | = 12; | z_{2} - 3 - 4 i | = 5

| z_{1} - z_{2} |

z_{1}, z_{2}

| z_{1} | = 12

| z_{2} - (3 + 4 i) | = 5

| z_{1} - z_{2} |

Join BYJU'S Learning Program