AP EAMCET · Maths · Hyperbola
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, then \((\mathrm{OA})^2-(\mathrm{OB})^2=\)
- A \(-\frac{20}{9}\)
- B \(\frac{16}{9}\)
- C \(-\frac{4}{9}\)
- D \(-\frac{4}{3}\)
Answer & Solution
Correct Answer
(A) \(-\frac{20}{9}\)
Step-by-step Solution
Detailed explanation
\(a^2 = 4, b^2 = 5\) \(e^2 = 1 + \frac{b^2}{a^2} = 1 + \frac{5}{4} = \frac{9}{4} \Rightarrow e = \frac{3}{2}\) Extremity of latus rectum in first quadrant \(P(ae, \frac{b^2}{a}) = (2 \cdot \frac{3}{2}, \frac{5}{2}) = (3, \frac{5}{2})\) Equation of tangent at…
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