Question

Which points are the foci of this hyperbola?

Answer 1

@Michele_Laino

Answer 2

((x - 1)^2)/8^2 - ((y - 2)^2)/6^2 = 1

Answer 3

(1, 2) and (11, 2)

(1, 2) and (1, 10)

(1, 12) and (1, –8)

(11, 2) and (–9, 2)

Answer 4

referring to the standard equation of the hyperbola:
\[\frac{{{X^2}}}{{{a^2}}} - \frac{{{Y^2}}}{{{b^2}}} = 1\]
we get:
a=8, and b=6
Now the x-coordinate of the foci are :
\[c = \pm \sqrt {{a^2} + {b^2}} = ...?\]

Answer 5

what are the values of c?

Answer 6

I got a 10

Answer 7

a ±10

Answer 8

ok!
so our foci are the points:
F1=(-c,0)=...?
and
F2=(c,0)=...?

Answer 9

(-10,0) (10,0)?

Answer 10

ok! that's right!

Answer 11

so what else I do?

Answer 12

we have finished!

Answer 13

none of the answers LOL

Answer 14

sorry you are right, since we have performed this traslation:
X=x-1
Y=y-2
so we have to solve this system:
x-1=10--->x=..?
and
x-1=-10---> x=...?

then we have to solve these equations:
y-2=0---< y=...?
y-2=0--->y=...?

Answer 15

x=11 x=-9

Answer 16

yes! and y=...?

Answer 17

y=2

Answer 18

thanks bro

Answer 19

thanks!