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

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

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