A circle S passes through the point (0, 1) and is orthogonal to the circles `(x -1)^2 + y^2 = 16` and `x^2 + y^2 = 1`. Then(A) radius of S is 8(B) radius of S is 7(C) center of S is (-7,1)(D) center of S is (-8,1)A. radius of S is 8B. radius of S is 7C. centre of S is (-7, 1)D. centre of S is (-8, 1)

A circle S passes through the point (0, 1) and is orthogonal to the ci

1.	A circle S passes through the point (0, 1) and is orthogonal to the circles `(x -1)^2 + y^2 = 16` and `x^2 + y^2 = 1`. Then(A) radius of S is 8(B) radius of S is 7(C) center of S is (-7,1)(D) center of S is (-8,1)A. radius of S is 8B. radius of S is 7C. centre of S is (-7, 1)D. centre of S is (-8, 1)
Answer» Correct Answer - B::C Let the circle S be `x^(2)+y^(2)+2gx+2fy+c=0`. It is orthogonal to the circles `x^(2) +y^(2)-2x-15=0` and `x^(2)+y^(2)-1=0`. Therefore, `2(gxx(-1)+fxx0)=c-15 and 2(gxx0+fxx0)=c-1` `rArr -2g=c-15 and c=1` `rArr c=1, g=7` The circle S passes through (0, 1). `:.` The circle S passes through (0, 1) `:. 1+2f+c=0 rArr f=-1` Thus, the centre of the circle S is (-7, 1) and radius is `sqrt(49+1-1)=7`. So, options (b) and (c) are correct.

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