The equation of normal to parabola y2=4ax at (at2,2at) is, y+tx=2at+at3 Consider the figure shown below.
Therefore, y2=4ax(
y+tx
2at+at3
) y2(2at+at3)=4ax(y+tx) 4atx2+4axy−(2at+at3)y2=0 since OP and OQ are at right angles, then the sum of coefficient of x2 and y2 is equal to zero. 4at−2at−at3=0 t2=2 t=±√2 Therefore, y=±√2x Hence, the slope of normal is ±√2.