The General Equation of Conic Sections — Quiz

Question 5 • Precalculus

What is the standard form of the following equation? 4 x squared plus 9 y squared plus 24 x minus 36 y plus 36 is equal to 0

Answer

the fraction with numerator open paren x plus 3 close paren squared and denominator 4 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 9 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 minus 2 close paren squared and denominator 9 is equal to 0

the fraction with numerator open paren x plus 3 close paren squared and denominator 9 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 4 is equal to 0

the fraction with numerator open paren x plus 3 close paren squared and denominator 9 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 4 is equal to 1

Explanation

Group the x-terms and y-terms, then complete the squares: 4(x² + 6x) + 9(y² − 4y) + 36 = 0. This becomes 4(x + 3)² + 9(y − 2)² = 36. Dividing by 36 gives (x + 3)²/9 + (y − 2)²/4 = 1, which is choice D.

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