An ellipse is represented by the equation the fraction with numerator open paren y minus 3 close paren squared and denominator 169 plus the fraction with numerator open paren x plus 6 close paren squared and denominator 144 is equal to 1 Each directrix of this ellipse is a ________________________ from the center on the major axis.

The larger denominator is 169 under the y-term, so the major axis is vertical and a = 13. For an ellipse, c² = a² − b² = 169 − 144 = 25, so c = 5; the directrices are a/e = a²/c = 169/5 = 33.8 units from the center. Since the major axis is vertical, the directrices are horizontal lines, making the correct choice “horizontal line that is 33.8 units.”

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