Practice Test

Question 5 • Precalculus

Convert 9 x squared plus 4 y squared minus 54 x minus 8 y minus 59 is equal to 0 into standard form.

Answer

the fraction with numerator open paren x plus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y plus 1 close paren squared and denominator 36 is equal to 1

the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y plus 1 close paren and denominator 9 is equal to 1

the fraction with numerator open paren x minus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y minus 1 close paren squared and denominator 36 is equal to 1

the fraction with numerator open paren x minus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 1 close paren and denominator 9 is equal to 1

Explanation

Group the x-terms and y-terms, then complete the square: 9(x² − 6x) + 4(y² − 2y) = 59 becomes 9(x − 3)² + 4(y − 1)² = 144. Divide both sides by 144 to get (x − 3)²/16 + (y − 1)²/36 = 1. This is choice C, with both squared terms centered at (3, 1).

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