A) a circle
B) a parabola
C) a straight line
D) a hyperbola
Correct Answer: A
Solution :
We have, \[P{{T}_{1}}=\mu P{{T}_{2}}\] (by condition) \[\Rightarrow \] \[{{\alpha }^{2}}+{{\beta }^{2}}+2{{g}_{1}}\alpha +2{{f}_{1}}\beta +{{c}_{1}}\] \[={{\mu }^{2}}\,({{\alpha }^{2}}+{{\beta }^{2}}+2{{g}_{2}}\alpha +2{{f}_{2}}\beta +{{c}_{2}})\] Hence, locus of \[(\alpha ,\,\,\beta )\] is \[({{x}^{2}}+{{y}^{2}})\,({{\mu }^{2}}-1)+2({{g}_{2}}{{\mu }^{2}}-{{g}_{1}})x\] \[+2\,({{f}_{2}}{{\mu }^{2}}-{{f}_{1}})\,y+{{c}_{2}}{{\mu }^{2}}-{{c}_{1}}=0\] Which is a circle.You need to login to perform this action.
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