Write this equation in standard form:
\[ 9x^2 - 4y^2 - 24y - 72 = 0 \]
Answer (2)
9 x 2 − 4 y 2 − 24 y − 72 = 0 9 x 2 − 4 y 2 − 24 y = 72 9 x 2 − ( 4 y 2 + 24 y + 36 ) = 72 − 36 9 x 2 − 4 ( y + 3 ) 2 = 36 36 9 x 2 − 36 4 ( y + 3 ) 2 = 36 36 4 x 2 − 9 ( y + 3 ) 2 = 1
The equation 9 x 2 − 4 y 2 − 24 y − 72 = 0 can be written in standard form as 4 x 2 − 9 ( y + 3 ) 2 = 1 after rearranging and completing the square. This process involves isolating terms and adjusting the equation to fit the standard form of a hyperbola. The resulting equation shows the relationship between x and y in a clear format.
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