If `ax + by = 1` is a normal to the parabola `y^2=4Px,` then prove that `Pa^3 + 2aPb^2=b^2.`

If the line px + qy =1 is a tangent to the parabola y^(2) =4ax, then

If the line px+qy=1 is a tangent to the parabola y^(2)=4ax. then

If x+y=k is a normal to the parabola y^(2)=12x then it touches the parabola y^(2)=px then

Equation of normal to the parabola y^(2)=4ax having slope m is

If x+y=k is a normal to the parabola y^(2)=12x, then it touches the parabola y^(2)=px then |P| =

The normals to the parabola y^(2)=4ax from the point (5a,2a) is/are

If the line (x)/(a)+(y)/(b)=1 be a normal to the parabola y^(2)=4px ,then the value of a/p -b^2/a^2

Statement 1: The line ax+by+c=0 is a normal to the parabola y^(2)=4ax. Then the equation of the tangent at the foot of this normal is y=((b)/(a))x+((a^(2))/(b)). Statement 2: The equation of normal at any point P(at^(2),2at) to the parabola y^(2)= 4ax is y=-tx+2at+at^(3)

The line sqrt(2)y-2x+8a=0 is a normal to the parabola y^(2)=4ax at P .then P =