Angle between tangents drawn from origin to parabola ${\mathrm{y}}^2=4\mathrm{a}(\mathrm{x}-\mathrm{a})$ is

${\mathrm{y}}^2=4\mathrm{a}(\mathrm{x}-\mathrm{a})$

point O= (0,0)

$$\begin{gathered} Any line pas\sin g through (0,0) is of the form y=mx \\ Since it is \tan gent to given parabola it meets parabola at two coincident points \\ sub y=mx in parabola we get \\ {m}^2{x}^2-4ax+4a^2=0 \\ roots of above equation are same \\ \Rightarrow 16a^2-16a^2{m}^2=0 \\ \Rightarrow m^2=1 \\ \Rightarrow m=\pm 1 \\ Here product of slopes =-1 \\ So,angle between \tan gents ={90}^0 \end{gathered}$$