wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

If x and y co-ordinates of a point P in the xy plane are given by x=(ucosα)t, y=(usinα)t12gt2 where t is a parameter and g,u and α are given constants. Then the locus of the point P is a parabola whose vertex is

A
(u2sinαcosαg,u2sin2α2g)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(u2sin2α2g,u2sinαcosαg)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(u2sinαcosα2g,u2sin2αg)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(u2sin2αg,u2sinαcosα2g)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (u2sinαcosαg,u2sin2α2g)
Eliminating the parameter t, we get
y=xtanα12g(x2u2cos2α)

x22xu2sinαcosαg=2u2cos2αgy
Adding u4sin2αcos2αg2 both sides, we get
(xu2sinαcosαg)2=2u2cos2αg(yu2sin2α2g)
It represents a parabola whose vertex is
(u2sinαcosαg,u2sin2α2g)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Parametric Representation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon