Question

The equation of a hyperbola is (x-2)^2/16 - (y+1)^2/9. Compare this equation with the standard equation of a hyperbola to find its attributes. Part A Find the values of a, b, c, h, and k and the coordinates of the center, vertices, and foci for the given hyperbola. (Hint: The vertices lie on the transverse axis and are at a distance of a unit from the center. The foci also lie on the transverse axis and are c units from the center.) please help!

Answer 1

The value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

What is hyperbola?

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have given a hyperbola equation:

$\rm \dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1$

We know the standard form of a hyperbola is given:

$\rm \dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$

After comparing:

a² = 16 ⇒ a = 4

b² = 9 ⇒ b = 3

$\rm c^2 = a^2+b^2\\\\\rm c^2 = 16+9 \Rightarrow 25$

c = 5

(h, k) is the center of the hyperbola:

(h, k) = (2, -1)

Vertices will be (a, 0) and (-a, 0):

(4, 0) and (-4,0)

Foci will be at (c, 0) and (-c, 0):

(5, 0) and (-5, 0)

Thus, the value of a, b, c, h, k, and foci coordinates are 4, 3, 5, 2, -1, and (5, 0) and (-5, 0) respectively.

 

Learn more about the hyperbola here:

brainly.com/question/12919612

#SPJ1

Answer 2

The value of a=4 , b=3 , k=-1 and h=2 for the hyperbola having the equation

$\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1$

What is hyperbola?

A hyperbola is the symmetrical open curve formed by the combination of a circular cone with a plane at a minimum angle with its axis than the side of the cone.

Here the general form of the equation of hyperbola will be:

$\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1$

And we have a equation given as:

$\dfrac{(x-2)^2}{16}-\dfrac{(y+1)^2}{9}=1$

By comparing the equation we the solutions

$a=4 , b=3 , k=-1 \ and\ h=2$

To know more about hyperbola follow

brainly.com/question/2351925

#SPJ1