A) \[\left( 1,0 \right)\]
B) \[\left( 0,1 \right)\]
C) \[\left( 0,-1 \right)\]
D) \[\left( -1,0 \right)\]
Correct Answer: D
Solution :
[d] The coordinate of extremities of the latus rectum of \[{{y}^{2}}=4x\] be (1, 2) and\[\left( 1,-2 \right)\]. So, the equation of the tangents at (1, 2) and \[\left( 1,-2 \right)\] be \[2y=\frac{4\left( x+ \right)}{2}\Rightarrow y=x+1\] ??...(1) \[-2y=\frac{4\left( x+ \right)}{2}\Rightarrow -y=x+1\] ?.......(2) Solving equation (1) and (2), we have \[2\left( x+1 \right)=0\] \[x=-1\]and \[y=0\] Thus, required point be (? 1, 0). Hence, option [d] is correct
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