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noname [10]
3 years ago
5

MEDAL AND POINTS!!!!! write equation: The hyperbola with center (1, 2), vertices (1, 5) and (1, –1) , and foci (1, 7) and (1, –3

).
Mathematics
1 answer:
telo118 [61]3 years ago
8 0
We notice the x of the foci don't change
that means the hyperbola opens up and down
\frac{(y-k)^2}{a^2}-  \frac{(x-h)^2}{b^2}=1
hmm
center is (1,2) and vertices (1,5) and (1,-1)
the distance to a vertex is 3, that is 'a'
the rectangle of refernce is 6 units high
remember that
a²+b²=c² where a is major axis, b is minor axis and c is the distance from focs to center
from focus to center is 5 units
a is 3
3²+b²=5²
9+b²=25
mnus 9
b²=16
sqrt
b=4


so
\frac{(y-2)^2}{3^2}-  \frac{(x-1)^2}{4^2}=1 is the equation
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Answer: The y-intercept (b) is 10.

Step-by-step explanation:

Use the slope and the point to help you. Plot the point (-3,4) on graphing paper or use geometry software. I use geometry software, it's easier.

You'll need to understand that the slope 2 can also be written as 2/1 (rise/run). Go up 2 units and go to the right 1 unit, then plot a point. Keep going until one of the points lies on the y-axis. The y-coordinate of that point is the y-intercept. So, the y-intercept (aka "b") is 10.

You're welcome, and I have a nice day! :D

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