Normal other than axis of parabola never passes from the focus

Find the lengths of the normals drawn to the parabola y^(2)=8ax from a point on the axis of the parabola at distance 8a from the focus

Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)^(2)+(5y+10)^(2)=(3x-4y+2)^(2) Statement 2: Normal to parabola never passes through its focus.

The focus of the parabola

Number of distinct normals of a parabola passing through the focus of the parabola is

If the normal drawn from the point on the axis of the parabola y^(2)=8ax whose distance from the focus is 8 a , and which is not parallel to either axes makes an angle theta with the axis of x ,then theta is equal to

If the normal drawn form the point on the axis of the parabola y^(2)=8ax whhose distance from the focus is 8 a , and which is not parallel to either axes . Makes an angle theta with the axis of x, then theta is equal to

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is

Equation of a normal to the parabola y^(2)=32x passing through its focus is