A) \[{{c}^{2}}-4=0\]
B) \[{{c}^{2}}-8=0\]
C) \[{{c}^{2}}-9=0\]
D) \[{{c}^{2}}-10=0\]
Correct Answer: C
Solution :
Homogenising the curve, we get \[{{x}^{2}}+{{y}^{2}}-2{{\left( \frac{y-2\sqrt{2}x}{c} \right)}^{2}}=0\] ?..(i) But lines represented by (i) are perpendicular. Hence coefficient of \[{{x}^{2}}+\]coefficient of \[{{y}^{2}}=0\] \[\Rightarrow 1-\frac{16}{{{c}^{2}}}+1-\frac{2}{{{c}^{2}}}=0\Rightarrow \frac{18}{{{c}^{2}}}=2\Rightarrow {{c}^{2}}-9=0\].
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