Graphing Parametric Equations — Quiz

Question 8 • Precalculus

Consider the parametric equations x is equal to 4 cosine t minus 3 and y is equal to 5 sine t plus 2 What is the rectangular form?

Answer

the fraction with numerator open paren x minus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y plus 2 close paren squared and denominator 25 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 5 is equal to 1

the fraction with numerator open paren x plus 3 close paren squared and denominator 16 plus the fraction with numerator open paren y minus 2 close paren squared and denominator 25 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 plus 2 close paren squared and denominator 5 is equal to 1

Explanation

From x = 4 cos t − 3, add 3 and divide by 4 to get cos t = (x + 3)/4. From y = 5 sin t + 2, subtract 2 and divide by 5 to get sin t = (y − 2)/5. Using cos²t + sin²t = 1 gives (x + 3)²/16 + (y − 2)²/25 = 1, which is choice C.

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