If the line x – 2y = 12 is tangent to the ellipse \(\frac{{{\text{x}}^{2}}}{{{\text{a}}^{2}}}+\frac{{{\text{y}}^{2}}}{{{\text{b}}^{2}}}=1\text{ }\!\!~\!\!\text{ at }\!\!~\!\!\text{ the }\!\!~\!\!\text{ point }\!\!~\!\!\text{ }\left( 3,\frac{-9}{2} \right)\), then the length of the latus rectum of the ellipse is:

If the line x – 2y = 12 is tangent to the ellipse \(\frac{{{\text{x}

1.	If the line x – 2y = 12 is tangent to the ellipse \(\frac{{{\text{x}}^{2}}}{{{\text{a}}^{2}}}+\frac{{{\text{y}}^{2}}}{{{\text{b}}^{2}}}=1\text{ }\!\!~\!\!\text{ at }\!\!~\!\!\text{ the }\!\!~\!\!\text{ point }\!\!~\!\!\text{ }\left( 3,\frac{-9}{2} \right)\), then the length of the latus rectum of the ellipse is:
A.	9
B.	12√2
C.	5
D.	8√3
Answer» B. 12√2

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