A) \[(-2,\,\,-6),\,\,(4,\,\,2)\]
B) \[(2,\,\,6),\,\,(-4,\,\,-2)\]
C) \[(-2,\,\,6),\,\,(-4,\,\,2)\]
D) none of the above
Correct Answer: A
Solution :
Given equation of line is\[4x-3y-10=0\] or \[y=\frac{4x-10}{3}\] ? (i) and equation of circle is \[{{x}^{2}}+{{y}^{2}}-2x+4y-20=0\] \[\Rightarrow \] \[{{x}^{2}}+{{\left( \frac{4x-10}{3} \right)}^{2}}-2x\] \[+4\left( \frac{4x-10}{3} \right)-20=0\] \[\Rightarrow \] \[{{x}^{2}}+\frac{(16{{x}^{2}}+100-80x)}{9}-2x\] \[+\frac{16x-40}{3}-20=0\] \[\Rightarrow \] \[25{{x}^{2}}-50x-200=0\] \[\Rightarrow \] \[{{x}^{2}}-2x-8=0\] \[\Rightarrow \] \[(x-4)(x+2)=0\] \[\Rightarrow \] \[x=4,\,\,-2\] On putting the values of x in Eq. (i), we get \[y=2,\,\,-6\] \[\therefore \]Required point of intersections are\[(-2,\,\,-6),\,\,(4,\,\,2)\].
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