Equation of the tangent at a point P on the parabola y2=4ax the normal at which is at a distancea 5 /4 from the focus of the parabola is

Equation of the normal with slop m isy=mx−2am−am3 whose distance from the focus(a,0) is am−2am−am31+m2=54a⇒16m21+m2=5⇒m2=1/4⇒m=±1/2Slope of the tangent is ± 2 and the equation of thetangent is y=±2x±a/2⇒4x±2y+a=0.