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Equation of the normal to parabola `y^(2)=4x` having slope m is <br> `y=mx-2m-m^(3)` <br> If it passes through the point (15, 12), then <br> `12=15m-2m-m^(3)` <br> `or" "m^(2)-13m+12=0` <br> Clearly, one root of the equation is 1. <br> `:." "(m-1)(m^(2)+m-12)=0` <br> `rArr" "(m-1)(m-3)(m+4)=0` <br> `rArr" "m=1,3,-4` <br> Thus, three normal can be drawn from (15, 12). <br> The equations of normal and corresponding points on the curve are given by <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_MATH_CG_3e_C05_S01_070_S01.png" width="80%">