The Vertex Of The Parabola y2 = 8x is At The Center Of A Circle And The Parabola Cuts The Circle At The Ends Of Its Latus Rectum. Then The Equation Of The Circle Is

The line  will touch the parabola y² = 4a(x + a), if

The equation of the parabola whose axis is vertical and passes through the points (0, 0), (3, 0) and (–1, 4), is

The points on the parabola y² = 36x whose ordinate is three times the abscissa are

The points on the parabola y² = 12x whose focal distance is 4, are

Axis of the parabola x² – 4x – 3y + 10 = 0 is  

The equation of the latus rectum of the parabola x² + 4x + 2y = 0 is 

x – 2 = t², y = 2t are the parameter equations of the parabola 

The equation  represents a parabola if  is

‘t₁’ and ‘t₂’ are two points on the parabola y² = 4x. If the chord joining them is a normal to the parabola at ‘t₁’ then

Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.