csat-suneung 2022 Q24 (Geometry)

csat-suneung · South-Korea · csat__math 3 marks Conic sections Eccentricity or Asymptote Computation

For a hyperbola $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { 6 } = 1$ with one focus at $( 3 \sqrt { 2 } , 0 )$, what is the length of the major axis? (Given that $a$ is a positive number.) [3 points]
(1) $3 \sqrt { 3 }$
(2) $\frac { 7 \sqrt { 3 } } { 2 }$
(3) $4 \sqrt { 3 }$
(4) $\frac { 9 \sqrt { 3 } } { 2 }$
(5) $5 \sqrt { 3 }$

For a hyperbola $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { 6 } = 1$ with one focus at $( 3 \sqrt { 2 } , 0 )$, what is the length of the major axis? (Given that $a$ is a positive number.) [3 points]\\
(1) $3 \sqrt { 3 }$\\
(2) $\frac { 7 \sqrt { 3 } } { 2 }$\\
(3) $4 \sqrt { 3 }$\\
(4) $\frac { 9 \sqrt { 3 } } { 2 }$\\
(5) $5 \sqrt { 3 }$

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