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If the points (0,4)a n d(0,2) are respec...

If the points `(0,4)a n d(0,2)` are respectively the vertex and focus of a parabola, then find the equation of the parabola.

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Given that the coordinates, vertex of the parabola (0,4) and focus of the parabola (0,2).

By defination of the parabola, PB=PF
`rArr abs((0+y-6)/(sqrt(0+1)))=sqrt((x-0)^(2)+(y-2)^(2))` ltbr. `rArr abs(y-6)=sqrt(x^(2)+y^(2)-4y+4)`
`rArr x^(2)+y^(2)-4y+4=y^(2)+36-12 y`
`rArrx^(2)+8y=32`
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