The straight line x + y = k touches the parabola y = x-x², if  k =

The locus of the midpoint of chords of the parabola y² = 4ax parallel to the line y = mx + c is

A straight line which makes equal intercepts on positive  X and Y axes and which is at a distance 1 unit from the origin intersects the straight line  y =2x+3+√2 at (x₀, y₀). Then 2x₀+y₀=

If the normals from any point to the parabola x² = 4y cuts the line  y = 2 in points whose abscissa are in A.P, then the slopes of the tangents at the 3 conormal points are in

The equation of the tangents drawn from (3,2)  to the parabola x² = 4y are

The line y =2x + k is a normal to the parabola y²= 4x,then=

The locus  of the point of intersection of perpendicular tangents to the parabola y²=4ax is

If a circle cuts the parabola y² = 4ax in four points, then the algebraic sum of oridinates of the four points is

The equation of the tangent to the parabola y² = 8x and which is parallel to the line x – y + 3 = 0

AB is a chord of the parabola y² = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projection of BC on the axis of the parabola is