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Find the equation of a parabola whose fo...

Find the equation of a parabola whose focus and vertex are (0, 0) and (0, 2) respectively.

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The focus (0,0) and vertex (0,2), of the parabola lie on Y-axis.
Produce SA + AZ
=2+2=4
Draw a perpendicular ZM from Z to the axis of parabola. ZM is the directrix of the parabola whose equation is y-4=0.
Let P(x,y) be any point on the parabola.
Now the equation of parabola
PS=PM
`sqrt((x-0)^(2)+(y-0)^(2))=y-4`
`rArr" "x^(2)+y^(2)=(y-4)^(2)`
`rArr" "x^(2)+y^(2)=y^(2)-8y+16`
`rArr" "x^(2)=-8(y-2)`.
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