Question

# If x and y co-ordinates of a point P in the xy plane are given by x=(ucosα)t, y=(usinα)t−12gt2 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)
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B
(u2sin2α2g,u2sinαcosαg)
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C
(u2sinαcosα2g,u2sin2αg)
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D
(u2sin2αg,u2sinαcosα2g)
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Solution

## The correct option is A (u2sinαcosαg,u2sin2α2g)Eliminating the parameter t, we get y=xtanα−12g(x2u2cos2α) ⇒x2−2xu2sinαcosαg=−2u2cos2αgy Adding u4sin2αcos2αg2 both sides, we get (x−u2sinαcosαg)2=−2u2cos2αg(y−u2sin2α2g) It represents a parabola whose vertex is (u2sinαcosαg,u2sin2α2g)

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