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=22
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 ± 22 = g2+f20+0+4