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Westkost [7]
3 years ago
10

Write the standard form of the equation of the hyperbola 4x2 − 9y2 − 16x − 36y − 56 = 0.

Mathematics
1 answer:
yarga [219]3 years ago
6 0
We have that
4x² − 9y²<span> − 16x − 36y − 56 = 0
</span>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(4x² -16x) +(− 9y²− 36y)= 56

(4x² -16x) -(9y²+36y)= 56

Factor the leading coefficient of each expression

4(x²-4x) -9(y²+4y)= 56

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

4(x²-4x+4) -9(y²+4y+4)= 56+16-36

4(x²-4x+4) -9(y²+4y+4)= 36

Rewrite as perfect squares

4(x-2)² -9(y+2)²= 36

divide by 36 both sides

[(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1

the answer is

The equation of the hyperbola in the standard form is

[(1/9)( x-2)^{2}]-[(1/4)( y+2)^{2}]=1

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Step-by-step explanation:

y = a (x − x₁) (x − x₂)

Expand:

y = a (x² − x₁x − x₂x + x₁x₂)

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Nellie took a total of 27 quizzes over the course of 3 weeks. After attending 4 weeks of school this quarter, how many quizzes w
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Read 2 more answers
for any positive integer n, the sum of the first n positive integers equals n(n 1)/2. what is the sum of all the even integers b
marusya05 [52]

The sum of all the even integers between 99 and 301 is 20200

To find the sum of even integers between 99 and 301, we will use the arithmetic progressions(AP). The even numbers can be considered as an AP with common difference 2.

In this case, the first even integer will be 100 and the last even integer will be 300.

nth term of the AP = first term + (n-1) x common difference

               ⇒    300 = 100 + (n-1) x 2

Therefore, n = (200 + 2 )/2 = 101

That is, there are 101 even integers between 99 and 301.

Sum of the 'n' terms in an AP = n/2 ( first term + last term)

                                                = 101/2 (300+100)

                                                = 20200

Thus sum of all the even integers between 99 and 301 = 20200

Learn more about arithmetic progressions at brainly.com/question/24592110

#SPJ4        

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