Question

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. Centre of $S$ is $(-7,1)$
• D. Centre of $S$ is $(-8,1)$

Answer 1

Answer: (B), (C)

The correct options are
B Radius of $S$ is $7$
C Centre of $S$ is $(-7,1)$

Given circles $x^2+y^2-2x-15=0$

$x^2+y^2-1=0$

Let equation of cirlce $x^2+y^2+2gx+2fy+c=0$

The circle passes through $(0,1)$

$\Rightarrow 1+2f+c=0$

Applying condition of orthogonality

$-2g=c-15,0=c-1$

$\Rightarrow c=1,g=7,f=-1$

$r=\sqrt{49+1-1}=7;centre(-7,1)$