Question

Graph the hyperbola with equation quantity x plus four squared divided by sixteen minus the quantity of y plus three squared divided by twenty five = 1.

Answer 1

Please see the attached figure. This is how you draw a hyperbola. Its general formula is:

(x-h)²/a² - (y-k)²/b² = 1, where

(h,k) is the center
a is the semi-major axis
b is the semi-minor axis

The given equation is

(x+4)²/16 - (y+3)²/25 = 1

So, from the general form we can deduce that,
Center(-4,-3)
a = 4
b = 5

So, the first point we can plot is the centerpoint. Next, you draw the two intersecting lines. Their slopes are +/- b/a. Thus, it corresponds to +/- 5/4. Using this slope, we can find the equation of the two lines by using the slope and the center.

-3 = +5/4 (-4) + b ---> b= 2
-3 = -5/4 (-4) + b ---> b= -8

So, you plot the equations y=5/4x + 2 and y = -5/4 x -8 by assigning values of x and plotting them against y. Then, the vertex of the hyperbolas are 4 units from the center, denoted by the green dots. The hyperbola is shown in the next picture.