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

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation:

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.