Math  /  Geometry

QuestionThe equation of the following conic section is (A) 9x2y2=369 x^{2}-y^{2}=36 (B) x29y2=36x^{2}-9 y^{2}=36 (C) x2+3y2=6x^{2}+3 y^{2}=6 (D) 9x2+y2=369 x^{2}+y^{2}=36 (E) x2+9y2=36x^{2}+9 y^{2}=36

Studdy Solution
Substitute a=6a = 6 and b=2b = 2 into the standard form:
x262+y222=1 \frac{x^2}{6^2} + \frac{y^2}{2^2} = 1 x236+y24=1 \frac{x^2}{36} + \frac{y^2}{4} = 1
Multiply through by 36 to eliminate the denominators:
x2+9y2=36 x^2 + 9y^2 = 36
The correct equation from the options is:
x2+9y2=36 \boxed{x^2 + 9y^2 = 36}

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