Answer:
\((x+5)^2=12(y-2)\)
Step-by-step explanation:
We are given that focus of parabola at (-5,5).
Equation of directrix y=-1
We have to derive the equation of parabola
We know that the parabola is the set of points (x,y) equally distant from (-5,5) and (x,-1).
Distance formula
\(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Apply this formula
\(\sqrt{(x+5)^2+(y-5)^2}=\sqrt{(x-x)^2+(y+1)^2}\)
Squaring on both sides then we get
\((x+5)^2+(y-5)^2=(y+1)^2\)
\((x+5)^2+y^2-10y+25=y^2+2y+1\) (\((a-b)^2=a^2+b^2-2ab,(a+b)^2=a^2+b^2+2ab\))
\((x+5)^2=y^2+2y+1-y^2+10y-25\)
\((x+5)^2=12y-24\)
\((x+5)^2=12(y-2)\)
This is required equation of parabola along y- axis.
