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Show that the parametric point (2+t^(2),...

Show that the parametric point `(2+t^(2),2t+1)` represents a parabola. Show that its vertex is (2,1).

Text Solution

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Given parametric equation are
`x=2+t^(2)` . . .(1)
`y=2t+1`
`rArr" "t=(y-1)/(2)`
From eq. (1)
`x=2+((y-1)/(2))^(2)`
`rArr" "x-2=((y-1)^(2))/(4)`
`rArr" "(y-1)^(2)=4(x-2)`
`rArr" "Y^(2)=4X`
which is the equation of a parabola. For the co-ordinates of vertex
`{:(,,,X=0_(,),Y=0),(rArr,,,x-2=0_(,),y-1=0),(rArr,,,x=2_(,),y=1):}`
Therefore, the co-ordinates of vertex = (2,1).
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