Length of the focal chord of the ellipse x²/a² + y²/b² = 1 which is inclined to the major axis at angle θ is

The length of the focal chord of an ellipse can be determined using a specific formula. For the ellipse given by the equation \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), the focal chord inclined at an angle \( \theta \) to the major axis has a length calculated as follows:

Formula for Length of Focal Chord

The length \( L \) of the focal chord is given by:

L = \frac{2b^2}{a \cos(\theta)}

Components Explained

• a: Semi-major axis of the ellipse.
• b: Semi-minor axis of the ellipse.
• θ: Angle of inclination to the major axis.

This formula shows how the length of the focal chord varies with the angle of inclination and the dimensions of the ellipse. The cosine function accounts for the angle's effect on the chord's length.