Match the following. Normals are drawn at points P Q and R lying on the parabola `y^2= 4x` which intersect at (3,0)

Normals are drawn at points A, B, and C on the parabola y^2 = 4x which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

If the normals drawn at the end points of a variable chord PQ of the parabola y^2 = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

If three normals are drawn from the point (c, 0) to the parabola y^(2)=4x and two of which are perpendicular, then the value of c is equal to

If tangents are drawn from points on the line x=c to the parabola y^2 = 4ax , show that the locus of intersection of the corresponding normals is the parabola. ay^2 = c^2 (x+c-2a) .

Normals at P, Q, R are drawn to y^(2)=4x which intersect at (3, 0). Then, area of DeltaPQR , is

Normals at P, Q, R are drawn to y^(2)=4x which intersect at (3, 0). Then, area of DeltaPQR , is

If the normals at two points P and Q of a parabola y^2 = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is

The number of normals drawn from the point (6, -8) to the parabola y^2 - 12y - 4x + 4 = 0 is

If y_(1),y_(2) are the ordinates of two points P and Q on the parabola and y_(3) is the ordinate of the intersection of tangents at P and Q, then

Statement 1: The point of intersection of the tangents at three distinct points A , B ,a n dC on the parabola y^2=4x can be collinear. Statement 2: If a line L does not intersect the parabola y^2=4x , then from every point of the line, two tangents can be drawn to the parabola.