Complete the square 9x^2-16y^2=144
To complete the square for this equation, let's first rearrange it to have the x's and y's on the left side:
9x^2 - 16y^2 = 144
Divide by 144:
(9x^2/144) - (16y^2/144) = 1
Dividing by 144 simplifies to:
x^2/16 - y^2/9 = 1
Now let's complete the square for both x and y terms:
For x^2/16:
We need to find a number to add to x^2/16 in order to complete the square. Take half of the coefficient of x, square it, and then add it to x^2/16:
(1/2)^2 = 1/4
Add 1/4 to both sides of the equation:
x^2/16 + 1/4 - y^2/9 = 1 + 1/4
x^2/16 + 1/4 - y^2/9 = 5/4
For y^2/9:
Similarly, take half of the coefficient of y, square it, and then add it to y^2/9 to complete the square:
- (1/2)^2 = -1/4
Add -1/4 to both sides of the equation:
x^2/16 + 1/4 - y^2/9 - 1/4 = 5/4 - 1/4
x^2/16 + 1/4 - y^2/9 - 1/4 = 1
Therefore, the completed square form of the given equation is:
(x^2/16 + 1/4)^2 - (y^2/9 + 1/4) = 1