Write the equation of the hyperbola with center (2,-5), vertex (2,-2), and focus (2+-5+2sqrt3)

Its A for sure :)

option A :

Step-by-step explanation:

the equation of the hyperbola with center (2,-5), vertex (2,-2), and focus (2+-5+2sqrt3)

center is (2,-5), vertex is (2,-2). It is a vertical hyperbola

General equation for vertical hyperbola is

Center (2,-5) so h=2, k= -5

vertex is (2,-2)

We know vertex is (h, k+a), k=-5

k + a= -2

-5 + a = -2

so a = 3

Given  focus (2+-5+2sqrt3)

Focus is (h , k+c), k= -5

Add 5 on both sides

We need to find out b

c^2 = a^2 + b^2

12 = 9 + b^2

b^2 = 3

we know a=3  so a^2 =9

we know h=2  and k = -5

Plug in all the values in general equation

glide reflection.

its mainly because the pattern will be infinite and will never end. it will look like a gilder or like a filpbook when set to motion.