If a normal chord at a point t on the parabola y^2=4 a x subtends a right angle at the vertex, then t equals to

Step-by-step solution

The perpendicular of the normal to the parabola y^2=4 a x at P is Suppose, it meets the parabola at Q . If O be the vertex of the parabola, then the combined equation of O P and O Q is a homogeneous equation of second degree. aligned & y^2=4 a x ( y+t x 2 a t+a t^3 ) & y^2 (2 a t+a t^3 )=4 a x(y+t x) & 4 a t x^2+4 a x y- (2 a t+a t^3 ) y^2=0 aligned Since, O P and O Q are at right angles, then Coefficient of x^2+ Coefficient of y^2=0 aligned & 4 a t-2 a t-a t^3 & =0 & t^2=2 t & = 2 aligned