Question

homework assignment 8.3 the parabola
due friday by 11:59pm points 13 submitting an external tool
homework assignment 8.3 the parabola
score: 4.35/13 answered: 7/13
question 8
write the equation of a parabola whose directrix is ( y = 1 ) and has a focus at ( (-10,-5) ).
question help: video written example

Explanation:

Step1: Find vertex coordinates

Vertex is midpoint of focus and directrix projection.
Focus $(-10,-5)$, directrix $y=1$. Midpoint y-coordinate: $\frac{-5+1}{2}=-2$. x-coordinate same as focus: $-10$. Vertex $(h,k)=(-10,-2)$.

Step2: Calculate $p$ value

$p$ = vertex y - focus y: $-2 - (-5)=3$ (or directrix y - vertex y: $1 - (-2)=3$, absolute value, sign: opens down since focus below directrix).

Step3: Write standard equation

Vertical parabola: $(x-h)^2=4p(y-k)$.
Substitute $h=-10,k=-2,p=-3$ (opens down so $p$ negative):
$(x+10)^2=4(-3)(y+2)$ → $(x+10)^2=-12(y+2)$.

Answer:

$(x + 10)^2 = -12(y + 2)$