Write the equation in standard conic form: 4y^2 - x^2 - 8y - 4x = 16.?

Answer 1

The key is completing the square.

4y^2 - x^2 - 8y - 4x = 16

First, group the x's and the y's with each other
4y^2 - 8y - x^2 - 4x = 16
Then, factor out the coefficient of the squared terms
4(y^2 - 2y) - (x^2 + 4x) = 16
Now, you're ready to "complete the square"
y^2 - 2y = (y - 1)^2 - 1
x^2 + 4x = (x + 2)^2 - 4
Now substitute the found expressions into the prior equation
4((y - 1)^2 - 1) - ((x + 2)^2 - 4) = 16
Now distribute the 4 and the -1 respectively
4(y - 1)^2 - 4 - (x + 2)^2 + 4 = 16
The -4 cancels out the +4
4(y - 1)^2 - (x + 2)^2 = 16
Now just divide both sides by 16 to get your final answer

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

Answer 2

I think you are looking at an hyperbolla

4y^2 - 8y -x^2 - 4x = 16
4(y^2 - 2y) - (x^2 + 4x) = 16
4(y^2 - 2y + 1) - (x^2 + 4x + 4) = 16 + 4 + 4
4(y - 1)^2 - (x + 2)^2 = 24
(4(y - 1)^2) / 24 - ((x + 2)^2) / 24 = 24/24
((y - 1)^2) / 6 - ((x + 2)^2) / 24 = 1

Answer 3

4y² - x² - 8y - 4x = 16
4(y² - 2y) - (x² + 4x) = 16
4(y² - 2y + 1) - (x² + 4x + 4) = 16 + 4*1 - 4

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

Answer 4

the common form of the equation of a circle is: (x - h)² + (y - ok)² = r² enable's improve the squares: x² - 2hx + h² + y² - 2ky + ok² = r² enable's write your equation with the 17 on the countless area and the words grouped on a similar time: x² + 4x + y² - 4y = 17 enable's upload an h² and a ok² to the two factors and found the prolonged regularly occurring form above it: x² - 2hx + h² + y² - 2ky + ok² = r² x² + 4x + h² + y² - 4y + ok² = 17 + h² + ok² we are able to come across h by matching + 4 and -2h: -2h = 4 h = -2 we are able to come across ok by matching -2k and -4: -2k = -4 ok = 2 consequently, ok² = 4 and h² = 4 x² - 2hx + h² + y² - 2ky + ok² = r² x² + 4x + 4 + y² - 4y + 4 = 17 + 4 + 4 Simplify the perfect area: x² + 4x + 4 + y² - 4y + 4 = 25 x² + 4x + 4 + y² - 4y + 4 = 5² all human beings be attentive to that x² + 4x + 4 will develop into (x - h)² and h = -2 so we are able to write the equation as: (x - {-2})² + y² - 4y + 4 = 5² (word: you're able to be able to write (x - {-2})² as (x + 2)² yet i don't advise it.) all human beings be attentive to that y² - 4y + 4 will develop into (y - ok)² and ok = 2 so we are able to write the equation as: (x - {-2})² + (y - 2)² = 5² complete.

Answer 5

work: 4(y^2-2y+1)-(x^2-4x+4)=16+4-4
4(y+1)^2-(x-2)^2=16

answer:
(y+1)^2 / 4 - (x-2)^2 / 16 =1

It's an hyperbola because of the subtraction sign.
a=2
b=4

Answer 6

1492

Answer 7

combine like terms them put in descending order w/ exponets