A) \[\frac{-20\pm \sqrt{155}}{11}:1\]
B) \[\frac{-2\pm 2\sqrt{155}}{11}:2\]
C) \[-20\pm 2\sqrt{155}:11\]
D) \[-20\pm \sqrt{155}:11\]
Correct Answer: C
Solution :
Let the point\[P(h,k)\]on the parabola divides the line joining\[A(4,-6)\]and B (3,1) in ratio\[\lambda :1\] Then, we have \[P(h,k)=\left( \frac{3\lambda +4}{\lambda +1},\frac{\lambda -6}{\lambda +1} \right)\] This point lies on the parabola. \[\therefore \] \[{{\left( \frac{\lambda -6}{\lambda +1} \right)}^{2}}=4\left( \frac{3\lambda +4}{\lambda +1} \right)\] \[\Rightarrow \] \[11{{\lambda }^{2}}+40\lambda -20=0\] \[\Rightarrow \] \[\lambda =\frac{-20\pm 2\sqrt{155}}{11}:1\]
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