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Question

Question: The locus of the centre of circles which pass through the centre of circle c<sub>1</sub> : x<sup>2</...

The locus of the centre of circles which pass through the centre of circle c1 : x2+ y2= 1 and touches the circle. c2 :x2 + y2 = 8.

A

x2+y2=22x^{2} + y^{2} = 2\sqrt{2}

B

x2+ y2 = 2

C

x2 + y2= 4

D

None of these

Answer

x2+ y2 = 2

Explanation

Solution

Let required equation of circle is

x2 + y2 + 2gx + 2fy + c = 0

\ c = 0

Q circle touches the circle x2 + y2 = 8 so equation of common tangent is 2gx + 2fy + 8 = 0. This is tangent to x2 + y2 = 8 also so ± 222 \sqrt { 2 } = 0+0+4 g2+f2\frac { 0 + 0 + 4 } { \sqrt { \mathrm {~g} ^ { 2 } + \mathrm { f } ^ { 2 } } }