Answer:
[tex]y=-\frac{223}{28}(x-8)^2-7[/tex]
Step-by-step explanation:
we are given a quadratic equation
we know that quadratic equation is same as equation of parabola
so, we can use formula
[tex]y=a(x-h)^2+k[/tex]
Focus is
[tex](h,k+\frac{1}{4a} )[/tex]
now, we can compare it with given focus
=(8,-8)
we get
[tex]h=8[/tex]
[tex]k+\frac{1}{4a}=-8[/tex]
Directrix is
[tex]y=k-\frac{1}{4a}[/tex]
we are given directrix =-6
[tex]k-\frac{1}{4a}=-6[/tex]
we got two equations as
[tex]k+\frac{1}{4a}=-8[/tex]
[tex]k-\frac{1}{4a}=-6[/tex]
now, we can add both equations
and we get
[tex]k+\frac{1}{4a}+k-\frac{1}{4a}=-8-6[/tex]
[tex]2k=-8-6[/tex]
[tex]2k=-14[/tex]
[tex]k=-7[/tex]
now, we can find 'a'
[tex]k+\frac{1}{4\times -7}=-8[/tex]
[tex]k=-\frac{223}{28}[/tex]
now, we can plug back all values
and we get
So, equation of parabola is
[tex]y=-\frac{223}{28}(x-8)^2-7[/tex]
