The circle cutting x2+y2−6x+4y−12=0 orthogonally and having centre (−1,2) is
If two circle having
radii r1 and r2 and centre at c1 and c2 cutting each
other orthogonally then,
cos(180−90∘)=r21+r22−(c1c2)22 r1r2=cos 90∘
∴r21+r22=(c1c2)2
Now, x2+y2−6x+4y−12=0
r1=√32+22+12=5,c1≡(3,−2)
And other circle has centre c2≡(−1,2)
∴r21+r22=c1c22
⇒(5)2+r22=(4√2)2
⇒r22=32−25
⇒r22=7
⇒r2=√7
So, equation of circle having centre at
c2≡(−1,2) and radius =√7 is
(x+1)2+(y−2)2=r22=7
⇒x2+y2+2x−4y−2=0