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Vertex (0,0), focus (3,0)...

Vertex (0,0), focus (3,0)

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Vertex
`O-=(0,0)`,
Focus S `-=(3,0)`
`:.OS=3`
`rArr` Distance of vertex O from directrix of vertex O from directrix OZ = 3
`rArr` Equation of directrix
`rArr` x+3=0
Let P(x,y) be a variable point on parabola. Now, distance of P from focus S
= perpendicular distance from P to the directrix
`rArr" "sqrt((x-3)^(2)+(y-0)^(2))=x+3`
`rArr" "(y+3)^(2)+y^(2)=(x-3)^(2)`
`rArry^(2)=12x`
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