The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola
$$
\frac{x^2}{4} - \frac{y^2}{5} = 1
$$
meets the x-axis and y-axis at $ A $ and $ B $ respectively. If $ O $ is the origin, find
$$
(OA)^2 - (OB)^2.
$$
Show Hint
- \( \frac{20}{9} \)
- \( \frac{16}{9} \)
- \( -\frac{4}{9} \)
- \( \frac{4}{3} \)
The Correct Option is A
Solution and Explanation
2. Equation of tangent at this point.
3. Calculate intercepts \( OA \) and \( OB \).
4. Compute \( (OA)^2 - (OB)^2 = \frac{20}{9} \).
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