Mathhhhhhh problem hyperbola standard form 4x^2-9y^2+32x-144y-548
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Mathhhhhhh problem hyperbola standard form 4x^2-9y^2+32x-144y-548

[From: ] [author: ] [Date: 12-04-09] [Hit: ]
Complete the square, be sure to multiply the addition by the lead coefficients.9..........
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
---------- -----------
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.
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keywords: Mathhhhhhh,standard,form,548,144,32,problem,hyperbola,Mathhhhhhh problem hyperbola standard form 4x^2-9y^2+32x-144y-548
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