First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
Answer:
i think its the second one
Step-by-step explanation:
First, you have to simplfy your equations, 2x+3y=3. Subtract 2x from both sides, get 3y=-2x+3. Divide each side by 3, get y=-2/3x+1.
Simplify your other equation, 2y=3x-4. Divide each side by 2, get y=3/2x-2.
Now you have your 2 equations, y=-2/3x+1, and y=3/2x-2. These lines are perpendicular if you make a graph and plot the lines.
The slope of the line is (6 - (-3))/(1 - (-5)) = 9/6 = 3/2, so by point slope form, the equation of the line is (y + 5) = 3/2(x + 3). Then 2y + 10 = 3x + 9, so 3x - 2y = 1. A + B + C = 3 + (-2) + 1 = 2.
