All categories

3 years ago

The equation y²/8² - x²/b² represents a hyperbola centered at the origin with a focus of (0, -10).

Mathematics

2 answers:

cestrela7 [59]3 years ago

6 0

Answer:

b = 6

Step-by-step explanation:

You probably already know the general equation from the my last couple of answer.

In this question, we have:

a=8

b= ?

c= -10 , c is the value of the foci

surprisingly, you can solve the value for a, b, and c using the same equation as the Pythagorean theorem.

c² = a² + b²

we need to solve for b so lets rearrange the equation.

b² = c² - a²

b = ±√(c² - a²)

b = ±√((-10)² - (8)²)

b = ±√(100 - 64)

b = ±√(36)

b = ±6

b = 6

blsea [12.9K]3 years ago

6 0

Answer: 6

Step-by-step explanation:

You might be interested in

Circle O, with center (x, y) passes through the points A(0, 0), B(-3, 0), and C(1, 2). Find the coordinates of the center of the

KonstantinChe [14]

Answer:

The center of the circle is

$(-\frac{3}{2},2)$

Step-by-step explanation:

Let the equation of the circle be

$x^2+y^2+2ax+2by+c=0$ , where (-a,-b) is the center of this circle.

The points lying the circle must satisfy the equation of this circle.

A(0,0)

We substitute this point to get;

$0^2+0^2+2a(0)+2b(0)+c=0$

$\implies c=0$

B(-3,0)

$(-3)^2+0^2+2a(-3)+2b(0)+c=0$

$\implies 9+0-6a+0+c=0$

$\implies -6a+c=-9$

But c=0

$\implies -6a=-9$

$\implies a=\frac{3}{2}$

C(1,2)

$1^2+2^2+2a(1)+2b(2)+c=0$

$1+4+2a+4b+c=0$

$2a+4b+c=-5$

Put the value of 'a' and 'c' to find 'b'

$2(\frac{3}{2})+4b+0=-5$

$3+4b+0=-5$

$4b=-5-3$

$4b=-8$

b=-2

Hence the center of the circle is

$(-\frac{3}{2},2)$

8 0

3 years ago

Solve for r in terms of s, t, and u. <br> t=u-s+r

Verdich [7]

Answer:

r = t - u - s

Step-by-step explanation:

To solve for r in terms of s, t, and u, means to have r on one side and have t, u, and s.

t = u - s + r

t - u = s + r

t - u - s = r

6 0

2 years ago

When do we flip an inequality?

tatuchka [14]

Answer:

When multiplying and dividing it by a negative

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Q={1,3,6,9,10,15} then rewrite in set builder method

AfilCa [17]

Answer:

{x:x is a multiple of 3, x ≤ 15}

4 0

2 years ago

You earned $34,000 and your total tax due was $6,200. what was your average tax rate?

nexus9112 [7]

6200 / 34000 = 0.1823....multiply by 100 to get ur percent
0.1823 * 100 = 18.23 rounds to 18% <=

5 0

3 years ago