Coordinate Geometry Question 120
Question: The position of a moving point in the XY-plane at time t is given by $ ( (u\cos \alpha )t,(u\sin \alpha )t-\frac{1}{2}gt^{2} ), $ where $ u,\alpha ,g $ are constants. The locus of the moving point is
Options:
A) A circle
B) A parabola
C) An ellipse
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ h=u\cos \alpha .t,k=u\sin \alpha .t-\frac{1}{2}gt^{2}, $ then $ t=\frac{h}{u\cos \alpha } $ .
Putting the value of t in $ k=u\sin \alpha .t-\frac{1}{2}gt^{2}, $ we get $ k=h\tan \alpha -\frac{1}{2}g\frac{h^{2}}{u^{2}{{\cos }^{2}}\alpha } $
$ \therefore $ Locus of (h, k) is $ y=x\tan \alpha -\frac{1}{2}g\frac{x^{2}}{u^{2}{{\cos }^{2}}\alpha } $ , which is a parabola.
BETA
