Question

write the equation of the hyperbola ( 36 x ^ { 2 } - 9 y ^ { 2 } - 72 x + 36 y - 324 = 0 ) in standard form

( \frac { ( x - h ) ^ { 2 } } { a ^ { 2 } } - \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1 ),

where:
( h = )
( k = )
( a = )
( b = )
question help: video written example

Explanation:

Step1: Group \(x\) and \(y\) terms

$$
LATEXBLOCK0
$$

Step2: Complete the square

For \(x\): \((x - 1)^{2}=x^{2}-2x + 1\), so \(x^{2}-2x=(x - 1)^{2}-1\)
For \(y\): \((y - 2)^{2}=y^{2}-4y + 4\), so \(y^{2}-4y=(y - 2)^{2}-4\)

$$
LATEXBLOCK1
$$

Step3: Divide by 324

$$
LATEXBLOCK2
$$

Answer:

\(h = 1\), \(k = 2\), \(a = 3\), \(b = 6\)