A) (5,2)
B) \[\left( -\frac{1}{2},-2 \right)\]
C) (5, ?2)
D) \[\left( \frac{3}{2},\,2 \right)\]
Correct Answer: C
Solution :
Given \[{{y}^{2}}=2(x-3)\] .....(i) Differentiate w.r.t. x, \[2y.\frac{dy}{dx}=2\Rightarrow \frac{dy}{dx}=\frac{1}{y}\] Slope of the normal \[=\frac{-1}{\left( \frac{dy}{dx} \right)}=-y\] Slope of the given line \[=2\] \[\therefore y=-2\] From equation (i), \[x=5\] \[\therefore \]Required point is \[(5,\,-2)\].
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