1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
deff fn [24]
3 years ago
15

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

solution .
Mathematics
1 answer:
pickupchik [31]3 years ago
3 0

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.

You might be interested in
The area of a rectangle is expressed as (14r + 21) square feet. If the width of the
lilavasa [31]

Answer:

 L  = 2r  + 3

Step-by-step explanation:

Given parameters:

Area of rectangle  = 14r + 21

Width of the rectangle  = 7ft

Unknown:

Length of the rectangle  = ?

Solution:

If the length of the rectangle is designated as L;

 Area of a rectangle = Length x width

Now insert the parameters:

           14r + 21   = L x 7

            L  = \frac{14r + 21}{7}  

           L  = 2r  + 3

8 0
3 years ago
How do I find angle a?
vfiekz [6]
The slope of the line is 2/3, so the angle is arctan(2/3) ≈ 33.69°.
8 0
3 years ago
A circle has a circumference of 144π. What is the radius of the circle?
Artist 52 [7]
To find the circumference of a circle you have to multiple the radius by 2 and also by pi. So, to find the radius when given just the circumference, who have to do the reverse operation and divide the circumference by 2 and also by pi to get the answer of 22.92993631, which you could of course round.
5 0
3 years ago
Please show all your work!!!
Alex73 [517]

Answer:

y= -6/5x -3

Step-by-step explanation:

So for now lets bring it into mx + b format

Subtract 6x from both sides to isolate y which is also called subtraction property of equality.

so 5y = -6x -15

Now you divide both sides by 5 which is called division property of equality.

You now have y = -6/5x - 3

y= -6/5x -3 is the slope intercept form of the standard form equation of 6x + 5y = -15.

Hope this helps!

3 0
2 years ago
On average, a commercial airplane burns about 3.9 × 10³ mL of gasoline per second. There can be as many as 5.1 × 10³ airplanes i
algol13
We use the given data above to calculate the volume of gasoline that is being burned per minute by commercial airplanes. 

Amount burned of 1 commercial airplane = <span>3.9 × 10³ ml of gasoline per second
Number of airplanes = </span><span>5.1 × 10³ airplanes

We calculate as follows:

</span> 3.9 × 10³ ml of gasoline per second / 1 airplane (5.1 × 10³ airplanes)(60 second / 1 min ) = <span>1.2 x 10^9 mL / min</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • Find the value for d<br> 2d - 5 = 17
    6·1 answer
  • 1. Find the possible values for s in the inequality 12s – 20 ≤ 50 – 3s – 25.
    6·2 answers
  • The local humane
    6·1 answer
  • During halftime of a football game, a slingshot launcher’s T-shirts at the crowd. A T-shirt is launch from a height of 3 feet wi
    5·1 answer
  • What is the slope of the equation y – 3 = –4(x – 5)?
    14·1 answer
  • PLZ HELP PLZ PLZ ILL MARK AS BRAINLIESTT!!
    12·1 answer
  • Which of the following can be used to find the volume?
    12·2 answers
  • 14 in. = _____ ft<br> Plzzzzzzzzzzzz help
    8·2 answers
  • The perimeter of a rectangular field is 318 yards. If the width of the field is 74 yards, what is its length?
    10·2 answers
  • Solve for X. No decimals <br> Help please
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!