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The set of points on the axis of the parabola \mathrm{ y^2-4 x-4 y+12=0} from which all three normals to the parabola are real is (k, m), where k and m is

Option: 1

k>4, m=2


Option: 2

k>5, m=0


Option: 3

k>4, m=1


Option: 4

None of these 


Answers (1)

best_answer

\mathrm{\begin{aligned} & y^2-4 x-4 y+12=0 \\ & y^2-4 y+4=4 x-8 \Rightarrow(y-2)^2=4(x-2) \\ & Y^2=4 X, Y=y-2, X=x-2 \end{aligned}}

All three normals to the parabola are real & meet the axis of parabola, therefore
X > 2a & Y = 0

\mathrm{\begin{aligned} & \Rightarrow X>2(1) \& y-2=0 \Rightarrow x-2>2 \& y=2 \\ & \Rightarrow x>4 \& y=2 \end{aligned}}

Point is (k, 2), k > 4

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Ritika Kankaria

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