how do we put x^2-2y^2=4 into a standard equation???
the only thing I would do it divide by 4
(x^2)/4 - (y^2)/4 = 1
so, hyperbola with a = 2, b=2
ok thanks just making sure..
To put the equation x^2 - 2y^2 = 4 into a standard form, you need to rearrange it in a way that isolates the variables on one side of the equation. The standard form for an equation of a conic section is generally written as Ax^2 + By^2 + Cx + Dy + E = 0, where A, B, C, D, and E are constants.
Here's how to convert x^2 - 2y^2 = 4 into standard form:
Step 1: Start by moving the constant term (the "4" in this case) to the other side of the equation:
x^2 - 2y^2 - 4 = 0
Step 2: Notice that the equation has both x^2 and y^2 terms, but the coefficients are not yet in standard form. To proceed, we need to factor out any common factors that are present in both terms. In this case, the common factor is -2:
x^2/(-2) + y^2/1 - 4 = 0
Step 3: Rewrite the equation by dividing both the x^2 term and the y^2 term by the coefficient of their respective variables, so that the coefficients become 1:
(x^2/(-2)) / (-1/2) + (y^2/1) / (-4/2) - 4 = 0
Simplifying this expression, we get:
(-2/2)x^2 + (1/2)y^2 - 4 = 0
Step 4: Finally, multiply through by -1 to make the x^2 term positive, which is typical in standard form:
(2/2)x^2 - (1/2)y^2 + 4 = 0
Simplifying this further, we have:
x^2/2 - y^2/2 + 4 = 0
So, the equation x^2 - 2y^2 = 4 can be expressed in standard form as x^2/2 - y^2/2 + 4 = 0.