Question

If a tangent having slope \( \frac{-4}{3} \) to the ellipse \[ \frac{x^2}{18} + \frac{y^2}{32} = 1 \] intersects the major and minor axes in points A and B respectively, then the area of \( \triangle OAB \) is equal to

• A. 48 sq units
• B. 32 sq units
• C. 24 sq units
• D. 64 sq units

Hint:

For tangents to ellipses, use the equation of the tangent and geometry of the ellipse to find the area of the triangle formed by the tangent and axes.

Answer 1

The Correct Option is A

Step 1: Using geometry of the ellipse.
The area of \( \triangle OAB \) can be calculated using the lengths of the major and minor axes and applying the appropriate geometric formulas for triangles.

Step 2: Conclusion.
The area of \( \triangle OAB \) is 48 sq units, corresponding to option (1).