Determine the equation of a conic section...(Hyperbola) Given: center (-9, 1) distance between displaystyle{F}{1}{quadtext{and}quad}{F}{2}={20} units distance between displaystyle{C}{V}{1}{quadtext{and}quad}{C}{V}{2}={4} units orientation = vertical

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-02-05

Determine the equation of a conic section...(Hyperbola) Given: center (-9, 1) distance between F1 and F2=20 units 
distance between CV1 and CV2=4 units orientation = vertical

Answer & Explanation

dieseisB

dieseisB

Skilled2021-02-06Added 85 answers

Step 1
Given: center (-9, 1)
distance between F1andF2=20 units
distance between CV1andCV2=4 units
orientation = vertical
Step 2
Standard equation of hyperbola
(yk)2a2(xh)2b2=1
where (h,k) is centre and orientation is vertical
We know distance between F1andF2=2C=20
so C=10 unit and c2=a2+b2
here center is (-9, 1)
h=9andk=1
length of CV1CV2=2b
2b=4 unit
b=2 unit
Now from c2=a2+b2
(10)2=a2+(2)2
1004=a2
a=96
Step 3
So the equation of hyperbola is
(y1)296(x+9)24=1
where (-9, 1) is centre
Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-27Added 2605 answers

Answer is given below (on video)

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