Statement 1: The normals at the points (4, 4) and `(1/4,-1)` of the parabola `y^2=4x` are perpendicular. Statement 2: The tangents to the parabola at the end of a focal chord are perpendicular.

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

Each question has four choices a, b, c and d, out of which only one is correct. Each question contains Statement 1 and Statement 2. Find the correct answer. Statement 1 : Slopes of tangents drawn from (4, 10) to theparabola y^2=9x are and 1/4 and 9/4 . Statement 2 : Two tangents can be drawn to a parabola from any point lying outside the parabola.

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.

Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

Find the equation of the tangents from the point (2,-3) to the parabola y^(2)=4x

Statement 1: The line joining the points (8,-8)a n d(1/2,2), which are on the parabola y^2=8x , passes through the focus of the parabola. Statement 2: Tangents drawn at (8,-8) and (1/2,2), on the parabola y^2=4a x are perpendicular.

Statement 1: There are no common tangents between the circle x^2+y^2-4x+3=0 and the parabola y^2=2xdot Statement 2:Given circle and parabola do not intersect.

Length of the shortest normal chord of the parabola y^2=4ax is