A) \[\left( -\frac{22}{9},-\frac{2}{9} \right)\]
B) \[\left( \frac{22}{9},\frac{2}{9} \right)\]
C) \[\left( -\,2,\,\,-2 \right)\]
D) none of these
Correct Answer: A
Solution :
[a] \[2{{x}^{2}}+{{y}^{2}}=12\] or \[\frac{dy}{dx}=-\frac{2x}{y}\]. Slope of normal at point A (2, 2) is\[\frac{1}{2}\]. Also, point \[B\left( -\frac{22}{9},-\frac{2}{9} \right)\]lies on the curve and slope of AB is \[\frac{2-(-2/9)}{2-(-22/9)}=\frac{1}{2}\] Hence, the normal meets the curve again at point \[\left( -\frac{22}{9},-\frac{2}{9} \right)\].
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