The equation of the axis of the parabola (y + 3)² = 4(x – 2) is

Two straight lines are perpendicular to each other. One of them touches the parabola y² = 4a (x + a) and the other touches y2 = 4b (x + b). the locus of the point of intersectionof the two lines is

The locus of the point of intersection of two tangents to the parabola y² = 4ax which make the angle θ₁ and θ₂ with the axis so that cot θ₁ + cos θ₂ = k is

The equation of the axis of the parabola (y + 3)² = 4(x – 2) is

The equation of the tangent to the parabola y² = 12x at (3, -6) is

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