Question

For an ellipse, the foci are \( F(3,0) \) and \( F'(-3,0) \). If the length of the minor axis is 8, then the length of the major axis is equal to

• A. \( 16 \)
• B. \( 15 \)
• C. \( 14 \)
• D. \( 12 \)
• E. \( 10 \)

Hint:

For an ellipse, use \( c^2 = a^2 - b^2 \) to find the semi-major and semi-minor axes.

Answer 1

Answer: (E)

For an ellipse, the standard relation holds: \[ c^2 = a^2 - b^2 \] where: - \( a \) is the semi-major axis, - \( b \) is the semi-minor axis, - \( c \) is the focal distance (distance from center to foci). From the given foci: \[ c = 3 \] Given that the minor axis is 8, we have: \[ b = \frac{8}{2} = 4 \] Using the equation: \[ c^2 = a^2 - b^2 \] \[ 3^2 = a^2 - 4^2 \] \[ 9 = a^2 - 16 \] \[ a^2 = 25 \] \[ a = 5 \] Since the major axis length is \( 2a \): \[ {Major Axis} = 2 \times 5 = 10 \] 
Final Answer: \[ \boxed{10} \]