Determine the equation of a conic section...(Hyperbola) Given: center (-9, 1) distance betweenF1andF2=20unitsdistance betweenCV1andCV2=4units orientation...

Step 1
Given: center (-9, 1)
distance between ${\displaystyle F1\text{and}F2=20}$ units
distance between ${\displaystyle CV1\text{and}CV2=4}$ units
orientation = vertical
Step 2
Standard equation of hyperbola
${\displaystyle \frac{{(y-k)}^2}{a^2}-\frac{{(x-h)}^2}{b^2}=1}$
where (h,k) is centre and orientation is vertical
We know distance between ${\displaystyle F1\text{and}F2=2C=20}$
so ${\displaystyle C=10\text{unit and}{c}^2=a^2+b^2}$
here center is (-9, 1)
${\displaystyle h=-9\text{and}k=1}$
length of ${\displaystyle CV1\to CV2=2b}$
${\displaystyle 2b=4}$ unit
${\displaystyle b=2}$ unit
Now from ${\displaystyle c^2=a^2+b^2}$
${\displaystyle {\left(10\right)}^2=a^2+{\left(2\right)}^2}$
${\displaystyle 100-4=a^2}$
${\displaystyle a=\sqrt{96}}$
Step 3
So the equation of hyperbola is
${\displaystyle \frac{{(y-1)}^2}{96}-\frac{{(x+9)}^2}{4}=1}$
where (-9, 1) is centre

Answer is given below (on video)