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Find the centre of the circle passing through (0,0) and (1,0) and touching the circle x²+y² = 9.

Find the centre of the circle passing through (0,0) and (1,0) and touching the circle x²+y² = 9.

Grade:12

1 Answers

Arun
25750 Points
3 years ago
Let the equation of circle is
x² + y² + 2gx + 2fy + c = 0
centre = (-g,-f)
radius = √(g²+f²-c)
it passes through (0,0)&(1,0) so point satisfy the equation 
put (0,0)
c = 0
put (1,0)
g = -1/2
since the circle touches internally hence
distance between centre = difference of radius
centre of given circle = (0,0)
radius = 3
√(g² + f²) = 3 - √(g²+f²-c)
√(1/4 + f²) = 3 - √(1/4 + f²)
√(1/4 + f²) = 3/2
1/4 + f² = 9/4
f² = 2
f = √2 or -√2
hence centre = (1/2,√2) or (1/2,-√2)
 
 

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