The equation of normal to the parabola y2=4ax is given by y=mx−2am−am3 Here, a=1 and point is (9,6) On putting a=1,x=9 and y=6 in the equation y=mx−2am−am3, we get ‌6=9m−2m−m3⇒m3−7m+6=0 ‌⇒m=−3,1,2 There are 3 distinct value of m. So, the number of normals will be 3 .
