Need help, I don’t understand this!

What is the coordinates of the center of an ellipse defined by the equation 16x^2 + 25y^2 + 160x - 200y + 400 = 0 ? Please give

pickupchik [31]

16x^2 + 25y^2 + 160x - 200y + 400 = 0     Rearrange and regroup.

(16x^2 + 160x) + (25y^2 - 200y ) = 0-400.     Group the xs together and the ys together.

16(X^2 + 10x) + 25(y^2-8y) = -400.     Factorising.

We are going to use completing the square method.

Coefficient of x in the first expression = 10.

Half of it = 1/2 * 10 = 5. (Note this value)

Square it = 5^2 = 25.     (Note this value)

Coefficient of y in the second expression = -8.

Half of it = 1/2 * -8 = -4. (Note this value)

Square it = (-4)^2 = 16. (Note this value)

We are going to carry out a manipulation of completing the square with the values

25 and 16. By adding and substracting it.

16(X^2 + 10x) + 25(y^2-8y) = -400

16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400

Note that +25 - 25 = 0.    +16 -16 = 0. So the equation is not altered.

16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = -400 +16(25) + 25(16)    Transferring the terms -16(25) and -25(16)

to other side of equation. And 16*25 = 400

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 25(16)

16(X^2 + 10x + 25) + 25(y^2-8y + 16) = 400

We now complete the square by using the value when coefficient was halved.

16(x-5)^2 + 25(y-4)^2 = 400

Divide both sides of the equation by 400

(16(x-5)^2)/400 + (25(y-4)^2)/400 = 400/400              Note also that, 16*25 = 400.

((x-5)^2)/25 + ((y-4)^2)/16 = 1

((x-5)^2)/(5^2) + ((y-4)^2)/(4^2) = 1

Comparing to the general format of an ellipse.

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1

Coordinates of the center = (h,k).

Comparing   with above   (x-5) = (x - h) , h = 5.

Comparing   with above   (y-k) = (y - k) , k = 4.

Therefore center = (h,k) = (5,4).

Sorry the answer came a little late. Cheers.

3 0

2 years ago

Someone help me on this

Advocard [28]

Answer:

idk

Step-by-step explanation:

8 0

2 years ago

Rudy, Maria, and Tito have a total of x textbooks Rudy has 6 textbooks andTito and Maria each have y textbooks. How many textboo

shtirl [24]

Answer:

Tito have $\frac{x-6}{2}$ textbooks in terms of x

Step-by-step explanation:

Rudy has 6 textbooks

We are given that Tito and Maria each have y textbooks

So, Tito has no. of books = y

Maria has no. of books = y

So, total number of textbooks = 6+y+y=6+2y

We are given that Rudy, Maria, and Tito have a total of x textbooks

So,6+2y=x

So, 2y=x-6

$y=\frac{x-6}{2}$

Hence Tito have $\frac{x-6}{2}$ textbooks in terms of x

6 0

2 years ago

What is the median 12,10,14,6,7

Nimfa-mama [501]

For this case we have that by definition, the median is the number of half in a set of numbers. To find it, the numbers are placed in order and the middle number is found.

If we order the given data we have:

6,7,10,12,14

The middle number is 10. So the median is 10.

Answer:

10

4 0

2 years ago

N is the middle integer of three consecutive positive integers.

abruzzese [7]

Answer :

$\boxed{\textsf{ The final answer is \textbf{n}$^{\textbf{3}}$ .}}$