A) \[{{x}^{2}}+{{y}^{2}}+xy-1=0\]
B) \[{{x}^{2}}+{{y}^{2}}-xy+1=0\]
C) \[{{x}^{2}}+{{y}^{2}}+xy+1=0\]
D) \[{{x}^{2}}+{{y}^{2}}-xy-1=0\]
Correct Answer: A
Solution :
Let (h, k) be point of intersection then \[\frac{h}{a}+\frac{k}{b}=1\] and \[ah+bk=1\] Also, it is given that\[{{a}^{2}}+{{b}^{2}}=1\]. Multiplying (i) and (ii), we get \[{{h}^{2}}+{{k}^{2}}+hk\left( \frac{b}{a}+\frac{a}{b} \right)=1\] or \[{{h}^{2}}+{{k}^{2}}+hk=1\] or \[{{x}^{2}}+{{y}^{2}}+xy-1=0\]
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