Question

Consider two points A and B on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$
circles are drawn having segments of tangents at A and B in between tangents at the two ends of major axis of ellipse as diameter, then the length of common chord of the circles is

• A. 8
• B. 6
• C. 10
• D.

Answer 1

The correct option is A 8

All such circles pass through foci $\therefore$ The common chord is of the length 2ae = $10\times \frac{4}{5}=8$