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Question: The circle x<sup>2</sup> + y<sup>2</sup> = 1 is completely contained in the circle x<sup>2</sup> + ...

The circle x2 + y2 = 1 is completely contained in the circle

x2 + y2 + 4x + 3y + k = 0, if

A

k< – 5

B

k < – 6

C

k < – 4

D

k < 0

Answer

k < – 6

Explanation

Solution

C1 (0,0) ; r1 = 1

C2(–2, –3/2) ; r2 =

̃ r2 = 254k\sqrt { \frac { 25 } { 4 } - \mathrm { k } }

one circle contained in the other then.

C1C2 < r2 – r1

52\frac { 5 } { 2 } < –1

̃ 72\frac { 7 } { 2 }

̃ 244\frac { - 24 } { 4 } ̃ k < – 6