which is the directrix of parabola with equation x^2=4y

Accepted Solution

Answer:[tex]y=-1[/tex]Step-by-step explanation:We have been given an equation of parabola [tex]x^2=4y[/tex]. We are asked to find the directrix of our given parabola.    First of all, we will divide both sides of our given equation by 4.[tex]\frac{x^2}{4}=\frac{4y}{4}[/tex]      [tex]\frac{x^2}{4}=y[/tex]      [tex]y=\frac{x^2}{4}[/tex]      Now, we will compare our equation with vertex form of parabola:[tex]y=a(x-h)^2+k[/tex], where, (h,k) represents vertex of parabola.We can see that the value of a is [tex]\frac{1}{4}[/tex], [tex]h=0[/tex] and [tex]k=0[/tex].Now, we will find distance of focus from vertex of parabola using formula [tex]p=\frac{1}{4a}[/tex].Substituting the value of a in above formula, we will get:[tex]p=\frac{1}{4*\frac{1}{4}}[/tex][tex]p=\frac{1}{1}=1[/tex]We know that directrix of parabola is [tex]y=k-p[/tex].Substituting the value of k and p in above formula, we will get:[tex]y=0-1[/tex][tex]y=-1[/tex]Therefore, the directrix of our given parabola is [tex]y=-1[/tex].