Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7

You can derive the formula which becomes...y=[1/(2(b-k))](x-a)^2+(1/2)(b+k)(a,b)=(-5,-5) and k=7 because y=7substitutey=[1/(2(-5-7))](x-[-5])^2+(1/2)(-5+7)y=[1/(-24)](x+5)^2+(1/2)(2)y=(-1/24)(x+5)^2+1 you can also do the following...the distance from the focus to a point is the same as the distance from the point to the directrix√(y-7)^2=√(x-[-5])^2+(y-[-5])^2square both sides and expandy^2-14y+49=x^2+10x+25+y^2+10y+25cancel each y^2 on both sides-14y+49=x^2+10x+25+10y+25-14y-10y=x^2+10x+25+25-49-24y=(x^2+10x+25)-24-24y=(x+5)^2-24divide both sides by -24y=(-1/24)(x+5)^2+1 again
so tell me if i helped

Answer x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​x=\frac{4(7+y)}{5}x=​5​​4(7+y)​​

step-by-step explanation: