A) \[\left( 8,\frac{15}{2} \right)\]
B) \[\left( -8,\frac{15}{2} \right)\]
C) \[\left( 8,-\frac{15}{2} \right)\]
D) None of these
Correct Answer: C
Solution :
Equations of circles \[{{x}^{2}}+{{y}^{2}}-8x+40=0\] ...(i) \[5{{x}^{2}}+5{{y}^{2}}-25x+80=0\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-5x+16=0\] ...(ii) and \[{{x}^{2}}+{{y}^{2}}-8x+16y+160=0\] ...(iii) Radical axis of Eqs. (i) and (ii), \[({{x}^{2}}+{{y}^{2}}-8x+40)-({{x}^{2}}+{{y}^{2}}-5x+16)=0\] \[\Rightarrow \] \[-8x+5x+40-16=0\] \[\Rightarrow \] \[3x=24\] \[\Rightarrow \] \[x=8\] Radical axis of Eqs. (i) and (iii), \[({{x}^{2}}+{{y}^{2}}-8x+40)-({{x}^{2}}+{{y}^{2}}-8x\] \[+16y+160)=0\] \[\Rightarrow \] \[-\text{ }8x+40+8x-16y-160=0\] \[\Rightarrow \] \[-16y-120=0\] \[\Rightarrow \] \[y=-\frac{120}{16}=-\frac{15}{2}\]\[\left( 8,-\frac{15}{2} \right)\] Thus, required point is
You need to login to perform this action.
You will be redirected in
3 sec
