A) intersect
B) are concentric
C) touch internally
D) touch externally
Correct Answer: C
Solution :
Equations of circles \[{{x}^{2}}+{{y}^{2}}-2x+6y+6\] ?(i) and \[{{x}^{2}}+{{y}^{2}}-5x+6y+15=0\] ?(ii) in equation(i)\[g=-1,f=3,c=6.\] Centre \[A=(1,-3)\] \[{{r}_{1}}=\sqrt{{{g}^{2}}+{{f}^{2}}-c}=\sqrt{1+9-6}=2\] in equation (ii), \[g=-5/2,f=3,c=15\] centre \[B=\left( \frac{5}{2},-3 \right)\] \[{{r}_{2}}=\sqrt{\frac{25}{4}+9-15}=\frac{1}{2},\] \[AB=\sqrt{{{\left( \frac{5}{2}-1 \right)}^{2}}+{{(-3+3)}^{2}}}=3/2\] and difference of radii \[({{r}_{1}}-{{r}_{2}})=2-\frac{1}{2}=3/2.\] Since distance between A and B is equal to \[{{r}_{1}}-{{r}_{2}},\]therefore the circles touch each other internally.
You need to login to perform this action.
You will be redirected in
3 sec
