Find the radius of the circle `(xcosalpha+ysinalpha-a)^2+(xsinalpha-ycosalpha-b)^2=k^2,ifalpha`varies, the locus of its centre is again a circle. Also,find its centre and radius.

Find the radius of the circle `(xcosalpha+ysinalpha-a)^2+(xsinalpha-yc

1.	Find the radius of the circle `(xcosalpha+ysinalpha-a)^2+(xsinalpha-ycosalpha-b)^2=k^2,ifalpha`varies, the locus of its centre is again a circle. Also,find its centre and radius.
Answer» `x&cos^2alpha+y^2sin^2alpha+a^2+2xysinalphacosalpha-2aysinalpha-2axcosalpha+x^2sin^2alpha+y^2cos^2alpha+b^2-2xysinalphacosalpha+2bycosalpha-2bxsinalpha=k^2` `x^2+y^2-2x(acosalpha-bsinalpha)+2y(bcosalpha-asinalpha)+a^2+b^2-k^2=0` `r=sqrt(g^2+f^2-c)` `r=sqrt((acosalpha+bsinalpha)^2+(bcosalpha-asinalpha)^2-a^2-b^2+k^2)` `r=sqrt(a^2+b^2+0-a^2-b^2+k^2` `r=k` `x=acosalpha+bsinalpha` `y=-(asinalpha-bcosalpha)` `x^2+y^2=a^2cos^2alpha+2ab sinalphacosalpha+b^2sin^2alpha+a^2sin^2alpha-2ab sinalphacosalpha+b^2cos^2alpha` `x^2+y^2=a^2+b^2` Circle r=`sqrt(a^2+b^2` `C=(0,0)`.