Circle: If a circle passes through the point (a,b) and cuts the circle… | AIEEE 2004

AIEEE 2004 (Offline)Question 1

If a circle passes through the point $(a,b)$ and cuts the circle $x^{2}+y^{2}=4$ orthogonally, then the locus of its centre is :

Circle

$2ax-2by-\left(a^{2}+b^{2}+4\right)=0$$2ax+2by-\left(a^{2}+b^{2}+4\right)=0$✓ Correct answer$2ax-2by+\left(a^{2}+b^{2}+4\right)=0$$2ax+2by+\left(a^{2}+b^{2}+4\right)=0$

Solution

With $x^2+y^2+2gx+2fy+c=0$: orthogonality gives $c=4$; passing through $(a,b)$ gives $a^2+b^2+2ga+2fb+4=0$, so the centre $(-g,-f)$ satisfies $2ax+2by-(a^2+b^2+4)=0$.

Circle - JEE Mathematics question (AIEEE 2004 (Offline))

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