Final answer:
To determine if a problem is in standard form, look at its equation. Rearrange the equation to match the standard form.
Step-by-step explanation:
In order to determine if a problem is in standard form, we need to look at its equation. The standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2.
Let's say we have an equation of a circle, such as x^2 + y^2 + 4x - 6y - 3 = 0.
To determine if this equation is in standard form, we need to rearrange it to match the standard form. We can start by grouping the x terms together and the y terms together, which gives us (x^2 + 4x) + (y^2 - 6y) = 3.
Next, we complete the square for both x and y. For x, we add (4/2)^2 = 4 to both sides of the equation, giving us (x^2 + 4x + 4) + (y^2 - 6y) = 7.
For y, we add (-6/2)^2 = 9 to both sides of the equation, giving us (x^2 + 4x + 4) + (y^2 - 6y + 9) = 7 + 4 + 9 = 20.
Finally, we can write the equation in standard form as (x + 2)^2 + (y - 3)^2 = 20.