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

If the vertex of the parabola y = x² – 8x + c lies on x – axis, then the value of c is

The equation of the parabola  with latusrectum joining the points (6,7) and (6,-1) is