write 196x^2-256y^2+17=12561 in standard form, show work.
Hmmm. Is it 17, or 17xy in the last term?
just 17, that's what got me confused to
196x^2 - 256y^2 = 12544
divide by 12544
x^2/64 - y^2/49 = 1
hyperbola
a = 8, b = 7
Thank you!:)
To write the equation 196x^2 - 256y^2 + 17 = 12561 in standard form, you need to have both the x and y terms separated and set equal to a constant. Here's how you can do it step by step:
Step 1: Move the constant term to the other side of the equation.
196x^2 - 256y^2 = 12561 - 17
Simplifying, you get:
196x^2 - 256y^2 = 12544
Step 2: Divide each term by the coefficient of x^2 to make the coefficient of x^2 1.
Dividing both sides of the equation by 196, you get:
x^2 - (256/196)y^2 = 12544/196
Step 3: Simplify the equation, if possible.
The fraction 256/196 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4. Simplifying further, you have:
x^2 - (64/49)y^2 = 12544/196
Step 4: Multiply through by the denominator to eliminate the fractions.
To eliminate the fractions, multiply both sides of the equation by 49. This gives us:
49(x^2) - 64y^2 = (12544/196) * 49
Step 5: Simplify the equation further, if possible.
The fraction (12544/196) * 49 can be simplified by multiplying the numerators and denominators, and then simplifying the resulting fraction. Simplifying it further, we have:
49(x^2) - 64y^2 = 784
Step 6: Rewrite the equation in standard form.
To write the equation in standard form, arrange the terms in descending order of degrees, with x^2 first and y^2 second. The constant term should be on the other side of the equation.
In this case, the equation in standard form is:
49x^2 - 64y^2 = 784