A) Hyperbola
B) Ellipse
C) Parabola
D) Circle
Correct Answer: B
Solution :
In question, \[PS=\frac{2}{3}PM\] (Given) Focus \[S(-2,\,0)\], Equation of directrix \[2x-9=0\] \[{{(PS)}^{2}}=\frac{4}{9}{{(PM)}^{2}}\] Þ \[{{(h+2)}^{2}}+{{(k)}^{2}}=\frac{4}{9}{{\left( \frac{2h-9}{2} \right)}^{2}}\] Þ \[9[{{(h+2)}^{2}}+{{(k)}^{2}}]=\frac{4{{(2h-9)}^{2}}}{4}\] Þ \[9{{h}^{2}}+9{{k}^{2}}+36h+36=4{{h}^{2}}+81+36h\] Þ \[\frac{5{{h}^{2}}}{45}+\frac{9{{k}^{2}}}{45}=1\] Þ \[\frac{{{h}^{2}}}{9}+\frac{{{k}^{2}}}{5}=1\] Þ 1 Locus of point P(h, k) is \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1\], which is an ellipse.You need to login to perform this action.
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