a circle passes through the point (a,b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is - Maths - Conic Sections

Question

a circle passes through the point (a,b) and cuts the circle
x2+y2=4 orthogonally, then the locus of its
centre is?

Ajanta Trivedi · Accepted Answer

let the equation of the circle which
passes through the point (a, b) is given by:
x2+y2+2gx+2fy+c=0  (1)a2+b2+2ga+2fb+c=0
(2)now circle (1) cuts the circle x2+y2=4 orthogonallytherefore2g*0+2f*0=c-4⇒c=4 
(3)substitute c=4 in eq(2):a2+b2+2g a+2f
b+4=0now let the centre of the circle by (h,k)therefore h=-g and k=-fthus 
a2+b2-2ha-2kb+4=0 replace h by x and k by y, thus the locus of the centre is:a2+b2-2xa-2yb+4=02(ax+by)-(a2+b2+4)=0
hope this helps you

a circle passes through the point (a,b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is?

a circle passes through the point (a,b) and cuts the circle x²+y²=4 orthogonally, then the locus of its centre is?