A) \[\left( \frac{11}{15},\ \frac{2}{25} \right)\]
B) \[\left( \frac{2}{25},\ \frac{11}{25} \right)\]
C) \[\left( \frac{11}{15},\ -\frac{2}{25} \right)\]
D) \[\left( -\frac{11}{25},\ -\frac{2}{25} \right)\]
Correct Answer: A
Solution :
Centre of conic is \[\left( \frac{hf-bg}{ab-{{h}^{2}}},\,\frac{gh-af}{ab-{{h}^{2}}} \right)\] \[=\frac{(-36)(-14)-(23)(-2)}{(2)(23)-{{(36)}^{2}}},\ \frac{(-2)(-36)-(2)(-14)}{(2)(23)-{{(-36)}^{2}}}\] \[=\left( -\frac{11}{25},\,-\frac{2}{25} \right)\].
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