Question:
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
$$
(OA)^2 - (OB)^2.
$$
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
Use hyperbola and tangent properties along with intercept form for calculations.
Updated On: Mar 18, 2026
- \( \frac{20}{9} \)
- \( \frac{16}{9} \)
- \( -\frac{4}{9} \)
- \( \frac{4}{3} \)
Show Solution
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The Correct Option is A
Solution and Explanation
1. Find coordinates of latus rectum extremity.
2. Equation of tangent at this point.
3. Calculate intercepts \( OA \) and \( OB \).
4. Compute \( (OA)^2 - (OB)^2 = \frac{20}{9} \).
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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