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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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
Solution
Let the centre of circle $S$ be $(h,k)$ and radius $r$.
Orthogonality condition with circle $x^2+y^2=1$:
$h^2 + k^2 = r^2 + 1$
Orthogonality with $(x-1)^2+y^2=16$:
$(h-1)^2 + k^2 = r^2 + 16$
Subtracting:
$(h-1)^2 - h^2 = 15$
$h^2 - 2h +1 - h^2 = 15$
$-2h = 14 \Rightarrow h = -7$
Since circle passes through $(0,1)$:
$r^2 = (0+7)^2 + (1-k)^2$
Using $h^2+k^2=r^2+1$:
$49 + k^2 = r^2 + 1$
Solving gives $k=1$.
Centre of $S = (-7,1)$
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