JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A square \(ABCD\) has all its vertices on the curve \(x ^{2} y ^{2}=1\). The midpoints of its sides also lie on the same curve. Then, the square of area of \(ABCD\) is
- A \(70\)
- B \(96\)
- C \(75\)
- D \(80\)
Answer & Solution
Correct Answer
(D) \(80\)
Step-by-step Solution
Detailed explanation
\(xy =1,-1\) \(\frac{t_{1}+t_{2}}{2} \cdot \frac{\frac{1}{t_{1}}-\frac{1}{t_{2}}}{2}=1\) \(\Rightarrow t_{1}^{2}-t_{2}^{2}=4 t_{1} t_{2}\) \(\frac{1}{t_{1}^{2}} \times\left(-\frac{1}{t_{2}^{2}}\right)=-1 \Rightarrow t_{1} t_{2}=1\)…
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