A) \[\frac{x}{3}-\frac{y}{2}=1,\ \frac{x}{2}+\frac{y}{3}=\frac{5}{6}\]
B) \[\frac{x}{3}+\frac{y}{2}=1,\ \frac{x}{2}-\frac{y}{3}=\frac{5}{6}\]
C) \[\frac{x}{2}+\frac{y}{3}=1,\ \frac{x}{3}-\frac{y}{2}=\frac{5}{6}\]
D) None of these
Correct Answer: A
Solution :
Given, equation of ellipse is \[4{{x}^{2}}+9{{y}^{2}}=36\] Tangent at point (3,?2) is \[\frac{(3)x}{9}+\frac{(-2)y}{4}=1\] or \[\frac{x}{3}-\frac{y}{2}=1\] \[\therefore \]Normal is \[\frac{x}{2}+\frac{y}{3}=k\] and it passes through point (3,?2) \[\therefore \]\[\frac{3}{2}-\frac{2}{3}=k\Rightarrow k=\frac{5}{6}\] \[\therefore \]Normal is, \[\frac{x}{2}+\frac{y}{3}=\frac{5}{6}\].
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