Question

Length of latus rectum of ellipse \[ \frac{x^2}{9} + \frac{y^2}{16} = 1 \]

Hint:

For ellipses, the formula for the latus rectum is derived from the semi-major and semi-minor axes. Ensure you are using the correct values for \(a\) and \(b\).

Answer 1

The length of the latus rectum for an ellipse is given by the formula: \[ \frac{2b^2}{a} \] where \(a\) is the semi-major axis and \(b\) is the semi-minor axis. Here, \(a^2 = 16\) and \(b^2 = 9\), so \(a = 4\) and \(b = 3\). Substituting these values into the formula gives: \[ \frac{2 \times 9}{4} = 4.5 \]