Question

the foci for the hyperbola (x-2)^2/36-(y+1)^2/64=1 is (2, -1+4sqrt(7) and (2,-1-4sqrt(7) true or false

Answer 1

how do you know what the foci is?

Answer 2

\[(2,-1+4\sqrt{7}) and (2,-1-4\sqrt{7})\]

Answer 3

\(\large \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) hyperbola with axis on x-axis, centred at origin

Answer 4

Foci are at \(\sqrt{a^2+b^2}\) from the origin.

Answer 5

Do you know where the centre of this hyperbola is?

Answer 6

(2,-1) i think

Answer 7

Good!
Does it have a horizontal or vertical axis?

Answer 8

idk :/ but i think its horizontal

Answer 9

Yes, because
\(\large \frac{x^2}{a^2}-\frac{y^2}{b^2}=-1\) hyperbola with axis on y-axis, centred at origin

Answer 10

So what are a, b and c=\(\sqrt{a^2+b^2}\)?

Answer 11

c= a=2 and b=-1

Answer 12

idk tbh

Answer 13

If you compare the equation of the standard ellipse with horizontal axis, you will find a^2=36, b^2=64, giving a=6, b=8, c=10.
And since the axis is horizontal, and hyperbola is centred at (h,k)=(2,-1)
we have the foci
(h+c,k), (h-c,k)