what is the standard form ! if you show the steps you get points
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Assuming 4x^2-9y^2+32x-144y-548=0 ?
Regroup 4x^2 +32x -9y^2 -144y= 548
Factor out lead coefficients: 4(x^2+8x)-9(y^2+ 16y)= 548
Complete the square, be sure to multiply the addition by the lead coefficients.
4(x^2+8x +16) -9(y^2+16y + 64)= 548 + 4(16) -9(64)
Factor: 4(x+4)^2 -9(y+8)^2 = 36
Divide all by 36
(x+4)^2 - (y+8)^2 =1
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9.......... ........4
Hoping this helps!
Regroup 4x^2 +32x -9y^2 -144y= 548
Factor out lead coefficients: 4(x^2+8x)-9(y^2+ 16y)= 548
Complete the square, be sure to multiply the addition by the lead coefficients.
4(x^2+8x +16) -9(y^2+16y + 64)= 548 + 4(16) -9(64)
Factor: 4(x+4)^2 -9(y+8)^2 = 36
Divide all by 36
(x+4)^2 - (y+8)^2 =1
---------- -----------
9.......... ........4
Hoping this helps!
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I will assume that the given expression is an equation equal to zero:
4x² - 9y² + 32x - 144y - 548 = 0
Standard form is:
(x - h)²/a - (y - k)²/b = 1
When (x - h)² is expanded, it equals x² + 2(-h)x + h²
When (y - k)² is expanded, it equals x² + 2(-k)x + k²
Group all of the x and y terms on the left and the constant on the right:
4x² + 32x - 9y² - 144y = 548
Factor 4 from the x terms and -9 from the y terms:
4(x² + 8x) - 9(y² + 16y) = 548
Complete the square for the x terms to look like the expanded square:
To find the value of h, we equate the x terms:
2(-h)x = 8x
h = -4
h² = 16
Add 4(16) to both sides:
4(x² + 8x + 16) - 9(y² + 16y) = 548 + 4(16)
We know that the x terms are a perfect square:
4(x - {-4})² - 9(y² + 16y) = 612
Complete the square for the y terms:
2(-k)y = 16y
k = -8
k² = 64
Add -9(64) to both sides:
4(x - {-4})² - 9(y² + 16y + 64) = 612 - 9(64)
We know that the y terms are a perfect square:
4(x - {-4})² - 9(y - {-8})² = 36
To force the right side to become 1, divide both sides by 36:
(x - {-4})²/9 - (y - {-8})²/4 = 1
This is standard form.
4x² - 9y² + 32x - 144y - 548 = 0
Standard form is:
(x - h)²/a - (y - k)²/b = 1
When (x - h)² is expanded, it equals x² + 2(-h)x + h²
When (y - k)² is expanded, it equals x² + 2(-k)x + k²
Group all of the x and y terms on the left and the constant on the right:
4x² + 32x - 9y² - 144y = 548
Factor 4 from the x terms and -9 from the y terms:
4(x² + 8x) - 9(y² + 16y) = 548
Complete the square for the x terms to look like the expanded square:
To find the value of h, we equate the x terms:
2(-h)x = 8x
h = -4
h² = 16
Add 4(16) to both sides:
4(x² + 8x + 16) - 9(y² + 16y) = 548 + 4(16)
We know that the x terms are a perfect square:
4(x - {-4})² - 9(y² + 16y) = 612
Complete the square for the y terms:
2(-k)y = 16y
k = -8
k² = 64
Add -9(64) to both sides:
4(x - {-4})² - 9(y² + 16y + 64) = 612 - 9(64)
We know that the y terms are a perfect square:
4(x - {-4})² - 9(y - {-8})² = 36
To force the right side to become 1, divide both sides by 36:
(x - {-4})²/9 - (y - {-8})²/4 = 1
This is standard form.