Graphing Polar Equations — Unit test

Question 19 • CUSD Advanced Math A (5.0)

Convert the equation –9x2 + 25y2 – 100y – 125 = 0 into standard form.

Answer

StartFraction (y + 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1

StartFraction (y minus 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1

StartFraction (y minus 2) squared Over 9 EndFraction minus StartFraction x squared Over 25 EndFraction = 1

StartFraction (y + 2) squared Over 5 EndFraction minus StartFraction 9 x squared Over 125 EndFraction = 1

Explanation

Group the y-terms and complete the square: 25(y² − 4y) − 9x² − 125 = 0 becomes 25(y − 2)² − 9x² = 225. Divide by 225 to get (y − 2)²/9 − x²/25 = 1. This matches choice C, with (y − 2)² over 9 and x² over 25.

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