Question

The product of perpendiculars from the two foci of the ellipse \[ \frac{x^2}{9} + \frac{y^2}{25} = 1 \] on the tangent at any point on the ellipse is:

• A. \( 6 \)
• B. \( 7 \)
• C. \( 8 \)
• D. \( 9 \)

Hint:

For standard ellipses, the product of perpendicular distances from the foci to any tangent is always equal to \( b^2 \).

Answer 1

The Correct Option is D

Step 1: Using the focal property of an ellipse For an ellipse, the product of the perpendicular distances from the foci to a tangent at any point is given by: \[ b^2. \] Here, \( a^2 = 25 \), \( b^2 = 9 \), so the product of the perpendicular distances is: \[ 9. \]