Find the following

Question

Use the equation (y+2)^2/4 - (x+3)^2/49 = 1 to find the following:

a. center
b. vertices
c. foci

d. graph it

Answer 1

The equation is

In the above equation y term is positive, then the hyperbola is vertical.

Compare it to  standard form of vertical hyperbola is

"a " is the number in the denominator of the positive term

center: (h, k ) Vertices: (h , k + a ), (h, k - a)

Foci: (h , k + c ), (h , k - c )

 Asympototes of hyperbola is

In this case a = 2, b = 7, 

a)

Center (h, k) = (-3,- 2)

b)

Vertices :

 (h , k + a ), (h, k - a)

(-3 , -2 + 2) ( -3 , - 2 - 2) = ( -3 , 0) ( -3 ,-4)

c)

Foci:

(h , k + c ), (h , k - c )

(-3, -2+7.28), ( -3.28, -2-7.28 ) = (-3,5.28) , (-3, -9.28)

 

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Answer 2

d) Graph

Asymptotes of hyperbola  are

Draw the coordinate plane.

Plot the center of hyperbola (-3,-2).

To graph the hyperbola go 2 units up and down from center point and 7 units left and right from center point(since a = 2, b = 7.)

Use these points to draw a rectangle .

Draw diagonal lines through the center and the corner of the rectangle. These are asymptotes.

Plot the vertices and foci of hyperbola.

Draw the curves, beginning at each vertex separately, that hug the asymptotes the farther away from the vertices the curve gets.

The graph approaches the asymptotes but never actually touches them.