A) \[3y=8x-10\]
B) \[3y-8x+7=0\]
C) \[8y+3x+7=0\]
D) \[3x+2y+7=0\]
Correct Answer: B
Solution :
\[\frac{x-{{x}_{1}}}{{{x}_{1}}/{{a}^{2}}}=\frac{y-{{y}_{1}}}{{{y}_{1}}/{{b}^{2}}}\], which is the standard equation of normal at point \[({{x}_{1}},\,{{y}_{1}})\]. In the given ellipse, \[{{a}^{2}}=20,\,{{b}^{2}}=\frac{180}{16}\]. Hence the equation of normal at the point \[(2,\,3)\] is \[\frac{x-2}{2/20}=\frac{y-3}{48/180}\] Þ \[40\,(x-2)=15(y-3)\] Þ \[8x-3y=7\]Þ \[3y-8x+7=0\].
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