A) 2
B) \[\sqrt{2}\]
C) 4
D) None of these
Correct Answer: A
Solution :
The equation of any normal to \[{{y}^{2}}=4ax\]at \[(a{{t}^{2}},2at)\]is \[y+tx=2at+a{{t}^{3}}\] ?(i) The combined equation of lines joining the vertex (origin) to the points of intersection of the parabola and line (i), is \[{{y}^{2}}=4ax\left( \frac{y+tx}{2at+a{{t}^{3}}} \right)\] \[\Rightarrow \] \[(2t+{{t}^{3}}){{y}^{2}}=4x(y+tx)\] Since, line (i) makes a right angle at the vertex, then coefficient of \[{{x}^{2}}+\]coefficient of \[{{y}^{2}}=0\] \[\Rightarrow \]\[4t-2t-{{t}^{3}}=0\] \[\Rightarrow \]\[{{t}^{2}}=2\]
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