Given:
[tex](y+2)^2=-4(x-7)[/tex]
Required:
We need to find the focus and directrix.
Explanation:
Consider the parabola equation.
[tex](y-k)^2=a(x-h)[/tex]
Compare this equation with the given equation.
[tex]We\text{ get }k=-2,\text{ h=7 and a =-4.}[/tex]
Consider the formula to find the focii.
[tex]Focii:(h+\frac{a}{4},k)[/tex]
Substitute h=7, a=-4, and k=-2 in the formula.
[tex]Focii:(7+\frac{-4}{4},-2)[/tex]
[tex]Focii:(7-1,-2)[/tex]
[tex]Focii:(6,-2)[/tex]
Consider the formula to find directrix.
[tex]x=h-\frac{a}{4}[/tex]
Substitute h=7, and a=-4 in the formula.
[tex]x=7-\frac{(-4)}{4}[/tex]
[tex]x=7-(-1)[/tex][tex]x=8[/tex]
Final answer:
[tex]Focii:(6,-2)[/tex]
[tex]x=8[/tex]
