Question

Let P, Q and R are three co-normal points on the parabola $y^2=4ax.$ Then the correct statements(s) is/are

• A. algebraic sum of the slopes of the normas at P ,Q and R vanishes
• B. algebraic sum of the slopes of the normals at P, Q and R vanishes
• C. centroid of the triangle PQR lies on the axis of the parabola
• D. All of these

Answer 1

The correct option is A algebraic sum of the slopes of the normas at P ,Q and R vanishes

Let P,Q,R are three coordinates on parabola $y^2=4ax$

The correct statement is :

$y=-xy+2at+a{t}^3$ is equation of normal of parabola $y^2=4ax$

$a{t}^3+(2a-x)t-y=0t_1+t_2+t_3=0$

Algebraic sum of slope of normals at $P,Q,R$ vanishes.