Hi, I need to determine the equation of a parabola given the focus (2,3) and the directrix y=-1(adsbygoogle = window.adsbygoogle || []).push({});

I sketched out a parabola opening up wards with a vertex of (1,1)

I made two distance equations one for any point on the parabola to the focus, and one distance from the directrix to any point on the parabola.

I equated the two equations

sqrt((x+2)^2 + (y+3)^2)) = sqrt((y+1)^2))

I took the square root of both sides and then tried to expand and simplify

I got [tex] x^2 - \frac {1} {4}x + \frac {9} {8} = y [/tex]

there probably are mistakes since this is my first time doing this.

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# Homework Help: Parabola equation with focus and directrix

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