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A point P\left ( t^{2}, t+1 \right ) moves in a plane. The locus of the point P is a conicsection whose equation is given by

Option: 1

x^{2}=y+1
 


Option: 2

y^{2}=x+1


Option: 3

x= \left ( y-1 \right )^{2}

 


Option: 4

none of these


Answers (1)

best_answer

as we learned

Conic sections locus -

A conic section is the locus of a point which moves in a plane so that its distance from fixed point is in a constant ratio to its perpendicular distance from a fixed straight line.

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Let\: \alpha = t^{2}, \beta = t+1\Rightarrow t=\beta -1\\*\\* \therefore \alpha = \left ( \beta -1 \right )^{2}\Rightarrow x= \left ( y-1 \right )^{2}i.e.\: a\: \: Parabola

 

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manish painkra

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