F.5 MATHS

5(a) S:(x-6)^2+(y+2)^2=9
Centre (6,-2) radius=3(b) Let Centre of C is (h,k)
Since the radius of C is h and the distance between the centres of two circles is equal to the sum of radius.(h-6)^2+(k+2)^2=(h+3)^2
h^2-12h+36+k^2+4k+4=h^2+6h+9
k^2-18h+4k+31=0Change h,k to x,y. The locus of the centre of circle C is
y^2-18x+4y+31=06(a) x'=2m/5 and y'=5n/2
=>m=5x'/2 and n=5y'/2(b) As P is on the circle x^2+y^2=4
(5x'/2)^2+(5y'/2)^2=4
25x'^2+25y'^2-16=0
Change x',y' to x,y. The locus of Q is 25x^2+25y^2-16=07 Let M(s,t) N(x,y)
Then a=(x+s)/2 and b=(y+t)/2
s=2a-x and t=2b-ySince M is on the circle x^2+y^2=r^2
(2a-x)^2+(2b-y)^2=r^2
x^2+y^2-4ax-4by+4a^2+4b^2-r^2=0 which is the locus of N