A) A parabola
B) An ellipse
C) A hyperbola
D) None of these
Correct Answer: B
Solution :
[b] Let the two fixed perpendicular straight lines be the co-ordinate axis let P(h, k) be the point whose locus is required Let \[PA:PB=1:2\] Then \[PA=\frac{\ell }{3}\] and \[PB=\frac{2\ell }{3}\] \[k=\frac{\ell }{3}sin\theta \] or \[3k=\ell \,sin\theta \] ?.... (i) and \[h=\frac{2\ell }{3}\cos \theta \] or \[\frac{3h}{2}=\ell \cos \theta \] .....(ii) Squaring and adding (i) and (ii) we get \[9{{k}^{2}}+\frac{9{{h}^{2}}}{4}={{\ell }^{2}}\] \[\therefore \text{ }locus~~~9{{x}^{2}}+36{{y}^{2}}=4{{\ell }^{2}}\] which is an ellipseYou need to login to perform this action.
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