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  • If the vertex of parabola is at (2,0) and the extremities of the latus rectum are (3,2) and (3,-2), then the equation of the parabola is  Option: 1</

If the vertex of parabola is at (2,0) and the extremities of the latus rectum are (3,2) and (3,-2), then the equation of the parabola is
 

Option: 1

\mathrm{y^2=2 x-4}


Option: 2

\mathrm{ x^2=4 y-8}


Option: 3

\mathrm{y^2=4 x-8}


Option: 4

none of these


Answers (1)

best_answer

The focus =\mathrm{\left(\frac{3+3}{2}, \frac{2-2}{2}\right)=(3,0)}. The vertex =(2,0) As \mathrm{ MV =\mathrm{VS}, \mathrm{M}=(1,0).}Clearly, the directrix is perpendicular to VS whose equation is \mathrm{ y=0}. So, the directrix is \mathrm{ x=k} which passes through \mathrm{M}(1,0). Therefore, we get \mathrm{ x=1}.

\therefore  the equation of the parabola is \mathrm{(x-3)^2+(y-0)^2=\left(\frac{x-1}{\sqrt{1}}\right)^2 }

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jitender.kumar

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