Find the lengths of the major and minor axes of the ellipse graphed by following equation. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$
A)Length of major axis is $2 a = 2 \cdot ( - 1 ) = - 2$ Length of minor axis is $2 b = 2 \cdot ( - 6 ) = - 12$
B)Length of major axis is $2 a = 2 \cdot 1 = 2$ Length of minor axis is $2 b=2 \cdot 6=12$
C)Length of major axis is $2 a = 2 \cdot ( - 6 ) = - 12$ Length of minor axis is $2 b = 2 \cdot ( - 1 ) = - 2$
D)Length of major axis is $2 a = 2 \cdot 6 = 12$ Length of minor axis is $2 b = 2 \cdot 1 = 2$
E)None of the above

Question

Find the lengths of the major and minor axes of the ellipse graphed by following equation.​ $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$ ​
A)Length of major axis is $2 a = 2 \cdot ( - 1 ) = - 2$ Length of minor axis is $2 b = 2 \cdot ( - 6 ) = - 12$
B)Length of major axis is $2 a = 2 \cdot 1 = 2$ Length of minor axis is $2 b=2 \cdot 6=12$
C)Length of major axis is $2 a = 2 \cdot ( - 6 ) = - 12$ Length of minor axis is $2 b = 2 \cdot ( - 1 ) = - 2$
D)Length of major axis is $2 a = 2 \cdot 6 = 12$ Length of minor axis is $2 b = 2 \cdot 1 = 2$
E)None of the above

Quizplus · Accepted Answer

The lengths of the axes of an ellipse are determined by the coefficients under the squared terms. For the given equation, the major axis length is $2a = 2\cdot6 = 12$ and the minor axis length is $2b = 2\cdot1 = 2$, corresponding to the square roots of the denominators in the equation.

Find the Lengths of the Major and Minor Axes of the Ellipse