The center of a hyperbola is (−2,4) , and one vertex is (−2,7) . the slope of one of the asymptotes is 12 .

what is the equation of the hyperbola in standard form?

The equation of the hyperbola in standard form is

Step-by-step explanation:

Given:

Centre of the hyperbola=(−2,4)

one vertex of the hyperbola= (−2,7) .

slope of the asymptote = 12

To Find:

The equation of the hyperbola in standard form=?

Solution:

W know that the  standard form of hyper bola is

............................(1)

where

(h,k) is the centre

(x,y) is the vertex of the parabola

a is the length between the centre and the vertices of the hyperbola

b is  the distance perpendicular to the transverse axis from the vertex to the asymptotic line

Now the length of a is given by

a=|k-y|

a=|4-7|

a=|-3|

a=3

Also we know that,

Slope == 2

=>

=>

=>b=1.5

Now substituting the known values in equation(1)

Step-by-step explanation:

The standard form of a hyperbola centered at a point distinct from origin has the following form:

The distance between the center and the vertex is:

The value of the other semiaxis is:

The standard equation of the hyperbola is:

b.an increase in a causes b to decrease

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10