A) \[{{90}^{o}}\]
B) \[{{30}^{o}}\]
C) \[{{\tan }^{-1}}\frac{1}{2}\]
D) \[{{45}^{o}}\]
Correct Answer: A
Solution :
Any line through origin is \[y=mx\]Since it is a tangent to \[{{y}^{2}}=4a(x-a),\]it will cut it in two coincident points. \ Roots of \[{{m}^{2}}{{x}^{2}}-4ax+4{{a}^{2}}=0\] are equal. \\[16{{a}^{2}}-16{{a}^{2}}{{m}^{2}}=0\]or \[{{m}^{2}}=1\]or \[m=1,-1\] Product of slopes\[=-1\]. Hence it is a right angled triangle.
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