Question侪 Write the equation in standard form for the hyperbola 믐 () 2 Submit
Studdy Solution
STEP 1
What is this asking? Rewrite the given equation for a hyperbola in its standard form. Watch out! Don't forget to complete the square correctly and keep track of those negative signs!
STEP 2
1. Prepare the Equation
2. Complete the Square for
3. Rewrite in Standard Form
STEP 3
Let's **group** our and terms together to get ready for completing the square!
We have .
Since there's no other term besides , let's just move the constant to the other side: .
STEP 4
To **complete the square** for the terms, we take the coefficient of the term (which is **12**), divide it by **2** (giving us **6**), and then square the result (giving us **36**).
This **36** is the special number we need!
STEP 5
We **add** this **36** to *both* sides of our equation: .
Now, the left side has a perfect square trinomial!
STEP 6
Let's **simplify** that equation: .
Lookin' good!
STEP 7
To get to **standard form**, we need a or on the right side.
So, let's **divide** both sides of the equation by **68**: .
STEP 8
Now, let's **simplify** those fractions: .
STEP 9
Almost there!
We want the positive term first, so let's **rearrange**: .
This is the standard form of the hyperbola equation!
STEP 10
The standard form of the given hyperbola equation is .
Was this helpful?