The length of the latus rectum of the parabola x² + 4x – 8y + 28 = 0 is

The equation of the axis of the parabola 3x² – 9x + 5y -2 = 0 is

The sub-tangent, ordinate and sub-normal to the parabola y² = 4ax at a point ( diffferent from the origin ) are in

The length of the chord intercepted bt the parabola y = x² + 3x  on the line x + y = 5 is

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 =