A) Straight line
B) Circle
C) Pair of straight lines
D) Parabola
Correct Answer: B
Solution :
Let the coordinates of the point P which divides the line joining (1, 0) and \[(2\cos \theta ,\,2\sin \theta )\]in the ratio \[2:3\] be\[(h,k)\]. Then, \[h=\frac{4\cos \theta +3}{5}\]and \[k=\frac{4\sin \theta }{5}\] Þ \[\cos \theta =\frac{5h-3}{4}\]and \[\sin \theta =\frac{5k}{4}\] Þ\[{{\left( \frac{5h-3}{4} \right)}^{2}}+{{\left( \frac{5k}{4} \right)}^{2}}=1\]Þ\[{{(5h-3)}^{2}}+(5{{k}^{2}})=16\] Therefore locus of \[(h,k)\]is \[{{(5x-3)}^{2}}+{{(5y)}^{2}}=16\],which is a circle.
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