Let P and Q be the points on the parabola y²=4 x so that the line segment P Q subtends right angle at the vertex. If P Q intersects the axis of the parabola at R, then the distance of the vertex from R is

Step-by-step solution

According to question, it is given that slope of P X and Q X are perpendicular to each other, i.e., slope of P X slope of X Q=-1 2 t t² 2 m m² =-1 t_ m =-4P Q: x-t² t²-m² = y-2 t 2 t-2 m Let P Q meets axis of parabola i.e, x -axis at R( , 0), then -t² (t+m)(t-m) = 0-2 t 2(t-m) -t²=-t²-t m=-t²+4 =4 A R=4